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JEE Differentiation PYQs with Solutions

190 previous year questions from Differentiation (JEE Main & Advanced Mathematics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

190 questionsMathematics2002–2026Answers + solutions

About Differentiation PYQs

Differentiation has 190 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 190 questions in this list come from JEE Main (87), NTA Abhyas JEE Main (46), 99 Percentile Qs Bank for JEE Main (30) and 2 other sources, spanning 2002 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

  • 2026: 4
  • 2025: 2
  • 2024: 11
  • 2023: 5
  • 2022: 8
  • 2021: 6
  • 2020: 56
  • 2019: 9
  • 2018: 4
  • 2017: 3
  • 2016: 1
  • 2014: 2

Differentiation questions with solutions

1

Let ℝ denote the set of all real numbers. Consider the polynomial function f: ℝ arrow ℝ defined by f(x) = d^ 10 dx^ 10 ((x^2 - 1)^ 10 ) , for all x ∈ ℝ . Here d^ 10 dx^ 10 ((x^2

JEE Advanced 2026 Solution View → 2

Let f(x) and g(x) be twice differentiable functions satisfying f''(x) = g''(x) for all x ∈ R , f'(1) = 2g'(1) = 4 and g(2) = 3f(2) = 9 . Then f(25) - g(25) is equal to :

JEE Main 2026 Solution View → 3

Let f be a real polynomial of degree n such that f(x) = f'(x) f''(x) , for all x ∈ ℝ . If f(0) = 0 , then 36(f'(2) + f''(2) + ∫_0^2 f(x)\,dx) is equal to:

JEE Main 2026 Solution View → 4

Let f(x)=x^ 3 +x^ 2 f^ (1)+2 x f^ (2)+f^ (3), x ∈ R . Then the value of f^ (5) is:

JEE Main 2026 Solution View → 5

Let ℝ denote the set of all real numbers. Let f: ℝ arrow ℝ and g: ℝ arrow(0,4) be functions defined by f(x)= _e(x^2+2 x+4) , and g(x)= 4 1+e^ -2 x Define the composite function f

JEE Advanced 2025 Solution View → 6

Let f: R arrow R be a twice differentiable function such that ( x y)(f(2 x+2 y)-f(2 x-2 y))=( x y)(f(2 x+2 y)+f(2 x-2 y)) , for all x, y ∈ R . If f^ (0)=(1)/(2) , then the value

JEE Main 2025 Solution View → 7

If _e y=3 ^ -1 x , then (1-x^2) y^ -x y^ at x=(1)/(2) is equal to

JEE Main 2024 Solution View → 8

Let f(x)=a x^3+b x^2+c x+41 be such that f(1)=40, f^ (1)=2 and f^ (1)=4 . Then a^2+b^2+c^2 is equal to:

JEE Main 2024 Solution View → 9

Suppose for a differentiable function h, h(0)=0, h(1)=1 and h^ (0)=h^ (1)=2 . If g(x)=h(e^x) e^ h(x) , then g^ (0) is equal to:

JEE Main 2024 Solution View → 10

If f(x)=\ array l x^3 ((1)/(x)), x ≠ 0 0 , x=0 array . then

JEE Main 2024 Solution View → 11

If y(θ)=(2 θ+ 2 θ)/( 3 θ+4 2 θ+5 θ+2) , then at θ=(π)/(2), y^ +y^ +y is equal to :

JEE Main 2024 Solution View → 12

Let f(x)=x^5+2 e^ x / 4 for all x ∈ R . Consider a function g(x) such that (g ∘ f)(x)=x for all x ∈ R . Then the value of 8 g^ (2) is :

JEE Main 2024 Solution View → 13

If y = ( x + 1)( x ^ 2 - x ) x x + x + x + (1)/(15)(3 ^ 2 x - 5) ^ 3 x, then 96 y ^ ' ((π)/(6)) is equal to:

JEE Main 2024 Solution View → 14

Let y = _ e ( 1 - x ^ 2 1 + x ^ 2 ), - 1 < x < 1 . Then at x = (1)/(2) , the value of 225( y ^ ' - y ^ " ) is equal to

JEE Main 2024 Solution View → 15

Suppose f(x) = ( 2 ^ x + 2 ^ - x )tanx ^ - 1 ( x ^ 2 - x + 1) (7 x ^ 2 + 3x + 1) ^ 3 . Then the value of f ^ ' (0) is equal to

JEE Main 2024 Solution View → 16

Let f ( x ) = x ^ 3 + x ^ 2 f ^ ' ( 1 ) + x f ^ " ( 2 ) + f ^ ''' ( 3 ) , x ∈ R . Then f ^ ' ( 10 ) is equal to

JEE Main 2024 Solution View → 17

Let for a differentiable function f: ( 0, ∞ ) → R , f(x) - f(y) ≥ _ e ((x)/(y)) + x - y, ∀ x, y ∈ (0, ∞) . Then ∑ _ n = 1 ^ 20 f ^ ' ( 1 n ^ 2 ) is equal to

JEE Main 2024 Solution View → 18

Let f(x) = sinx + cos - 2 sinx - cosx , x ∈ [0, π] - \ (π)/(4)\ , then f((7π)/(12)) f ^ " ((7π)/(12)) is equal to

JEE Main 2023 Solution View → 19

If 2 x ^ y + 3 y ^ x = 20, then (dy)/(dx) at (2, 2) is equal to:

JEE Main 2023 Solution View → 20

If y(x) = x ^ x , x > 0 , then y ^ " (2) - 2 y ^ ' (2) is equal to :

JEE Main 2023 Solution View → 21

Let y = f(x) = ^ 3 ((π)/(3)(cos( π 3 2 (- 4 x ^ 3 + 5 x ^ 2 + 1)(3)/(2)))) . Then, at x = 1 ,

JEE Main 2023 Solution View → 22

Let y(x) = (1 + x)(1 + x ^ 2 )(1 + x ^ 4 )(1 + x ^ 8 )(1 + x ^ 16 ) . Then y ^ ' - y ^ " at x = - 1 is equal to

JEE Main 2023 Solution View → 23

Let x(t) = 2 2 cost sin2t and y(t) = 2 2 sint sin2t , t ∈ (0, (π)/(2)) . Then 1 + ((dy)/(dx)) ^ 2 d ^ 2 y dx ^ 2 at t = (π)/(4) is equal to

JEE Main 2022 Solution View → 24

For the curve C: ( x ^ 2 + y ^ 2 - 3) + ( x ^ 2 - y ^ 2 - 1) ^ 5 = 0 , the value of 3 y ^ ' - y ^ 3 y ^ ' ' , at the point (α, α), α > 0 , on C , is equal to ________.

JEE Main 2022 Solution View → 25

The value of _ e 2(d)/(dx)( _ cosx cosec x) at x = (π)/(4) is

JEE Main 2022 Solution View → 26

If y(x) = ( x ^ x ) ^ x , x > 0 then d ^ 2 x d y ^ 2 + 20 at x = 1 is equal to

JEE Main 2022 Solution View → 27

If ^ - 1 ((y)/(2)) = _ e ((x)/(5)) ^ 5 , |y| < 2 , then

JEE Main 2022 Solution View → 28

Let f: ℝ → ℝ satisfy f(x + y) = 2 ^ x f(y) + 4 ^ y ( f(x), ∀ x , y ∈ ℝ . If f(2) = 3 , then 14 · f ^ ' (4) f ^ ' (2) is equal to _____.

JEE Main 2022 Solution View → 29

Let f: R → R be defined as f(x) = x ^ 3 + x - 5 . If g(x) is a function such that f(g(x)) = x, ∀ x ∈ R , then g ^ ' (63) is equal to ______

JEE Main 2022 Solution View → 30

If y = ^ - 1 (sec x ^ 3 - tan x ^ 3 ), (π)/(2) < x ^ 3 < (3π)/(2) , then

JEE Main 2022 Solution View → 31

If y ( x ) = cot ^ - 1 ( 1 + sinx + 1 - sinx 1 + sinx - 1 - sinx ), x ∈ ((π)/(2), π) , then (dy)/(dx) at x = (5π)/(6) is:

JEE Main 2021 Solution View → 32

If y ^ 1 / 4 + y ^ - 1 / 4 = 2x, and ( x ^ 2 - 1) d ^ 2 y d x ^ 2 + (dy)/(dx) + = 0, then | α - β | is equal to _______.

JEE Main 2021 Solution View → 33

Let f ( x ) = cos(2 ^ - 1 sin( cot ^ - 1 (1 - x)/(x) )), 0 < x < 1 . Then:

JEE Main 2021 Solution View → 34

If y = y ( x ) is an implicit function of x such that _ e ( x + y ) = 4xy , then d ^ 2 y d x ^ 2 at x = 0 is equal to

JEE Main 2021 Solution View → 35

If f(x) = sin( ^ - 1 ( 1 - 2 ^ 2x 1 + 2 ^ 2x )) and its first derivative with respect to x is - (b)/(a) _ e 2 when x = 1, where a and b are integers, then the minimum value of | a

JEE Main 2021 Solution View → 36

Let f: S → S where S = (0, ∞) be a twice differentiable function such that f(x + 1) = xf(x) . If g: S → R be defined as g(x) = _ e f(x) , then the value of | g ^ '' (5) - g ^ ''

JEE Main 2021 Solution View → 37

The derivative of ^ - 1 ( 1 + x ^ 2 - 1 x ) with respect to ^ - 1 ( 2x 1 - x ^ 2 1 - 2 x ^ 2 ) at x = (1)/(2) is :

JEE Main 2020 Solution View → 38

If (a + 2 bcosx ) ( a - 2 bcosy) = a ^ 2 - b ^ 2 , where a > b > 0, then (dx)/(dy) at ((π)/(4), (π)/(4)) is:

JEE Main 2020 Solution View → 39

If y ^ 2 + _ e ( ^ 2 x) = y, x ∈ (- (π)/(2), (π)/(2)) then :

JEE Main 2020 Solution View → 40

If x = 2sinθ - sin2θ and y = 2cosθ - cos2θ, θ ∈ [0, 2π], then d ^ 2 y d x ^ 2 at θ = π is:

JEE Main 2020 Solution View → 41

Let f and g be differentiable functions on R such that fog is the identity function. If for some a, b ∈ R, g ^ ' (a) = 5 and g(a) = b, then f ^ ' (b) is equal to:

JEE Main 2020 Solution View → 42

Let f be any function continuous on [a, b] and twice differentiable on (a, b) . If all x ∈ (a, b), f ^ ' (x) > 0 and f ^ '' (x) < 0 , then for any c ∈ (a, b), (f(c) - f(a))/(f(b)

JEE Main 2020 Solution View → 43

Let f(x) = (sin( ^ - 1 x) + sin( cot ^ - 1 x)) ^ 2 - 1 , |x| > 1 . If (dy)/(dx) = (1)/(2)(d)/(dx)( ^ - 1 (f(x))) and y( 3 ) = (π)/(6), then y(- 3 ) is equal to:

JEE Main 2020 Solution View → 44

Let y = y(x) be a function of x satisfying y 1 - x ^ 2 = k - x 1 - y ^ 2 where k is a constant and y((1)/(2)) = - (1)/(4) .Then (dy)/(dx) at x = (1)/(2) , is equal to

JEE Main 2020 Solution View → 45

If y(α) = 2( tanα + cotα 1 + ta n ^ 2 α ) + 1 si n ^ 2 α , α ∈ ((3π)/(4), π) , then (dy)/(dα) at α = (5π)/(6) is

JEE Main 2020 Solution View → 46

Let x ^ k + y ^ k = a ^ k , (a, k > 0) and (dy)/(dx) + ((y)/(x))(1)/(3) = 0, then k is

JEE Main 2020 Solution View → 47

If y = _ 10 ⁡ x + _ x ⁡ 10 + _ x ⁡ x + _ 10 ⁡ 10, then (dy)/(dx) is equal to

NTA Abhyas JEE Main 2020 Solution View → 48

If f(x) = \ cases x + 1; & x > 1 0; & x = 1 7 - 3x; & x < 1 cases ) then f^ ′ (0) equals to

NTA Abhyas JEE Main 2020 Solution View → 49

If _ 10 ⁡ ( x^ 3 - y^ 3 x^ 3 + y^ 3 ) = 2 , then (dy)/(dx) =

NTA Abhyas JEE Main 2020 Solution View → 50

Let ϕ ( x ) be the inverse of the function f ( x ) and f^ ′ (x) = 1 1 + x^ 5 , then (d)/(dx) ϕ (x) is equal to

NTA Abhyas JEE Main 2020 Solution View → 51

If y = ^ - 1 (secx - tanx), then the value of (dy)/(dx) is

NTA Abhyas JEE Main 2020 Solution View → 52

The differential coefficient of _ 10 ⁡ x with respect to _ x 10 is

NTA Abhyas JEE Main 2020 Solution View → 53

If l n (x + y) = 2 x y ,then y^ ′ (0) is equal to

NTA Abhyas JEE Main 2020 Solution View → 54

Let y = x^ x^ x … ∞ , then (dy)/(dx) is equal to (given x > 0 )

NTA Abhyas JEE Main 2020 Solution View → 55

If 2y = ( ^ -1 ⁡ ( 3 cos ⁡ x + sin ⁡ x cos ⁡ x - 3 sin ⁡ x ))^ 2 ∀ x ∈ (0, (π)/(2)), then (dy)/(dx) is equal to

NTA Abhyas JEE Main 2020 Solution View → 56

The rate of change of ( x^ 2 + 16 ) with respect to (x)/(x - 1) at x = 3 is

NTA Abhyas JEE Main 2020 Solution View → 57

If y = ^ - 1 ( 1 x ^ 2 + x + 1 ) + ^ - 1 ( 1 x ^ 2 + 3x + 3 ) + ta n ^ - 1 ( 1 x ^ 2 + 5x + 7 ) + ta n ^ - 1 ( 1 x ^ 2 + 7x + 13 ), x > 0 and ((dy)/(dx)) _ x = 0 = (- k)/(1 + k)

NTA Abhyas JEE Main 2020 Solution View → 58

If f(x) = cos ⁡ x. cos ⁡ 2x. cos ⁡ 4x. cos ⁡ 8x. cos ⁡ 16x , then f^ ' ((π)/(4)) is ( wheref^ ' ( x ) = (d)/(dx) f( x ) )

NTA Abhyas JEE Main 2020 Solution View → 59

If x = 1 - t^ 2 1 + t^ 2 and y = 2t 1 + t^ 2 , then(dy)/(dx) is equal to

NTA Abhyas JEE Main 2020 Solution View → 60

If u = x^ 2 + y^ 2 and x = s + 3t, y = 2s - t, then& d^ 2 u ds^ 2 is equal to (where t & is a constant)

NTA Abhyas JEE Main 2020 Solution View → 61

If y = acos ⁡ ( log ⁡ x ) + bsin ⁡ ( log ⁡ x ) , where a and b are& parameters, then x^ 2 y^ &#34; + xy^ &#39; is equal to

NTA Abhyas JEE Main 2020 Solution View → 62

If y = (lnx)/(x) , then d^ 2 y dx^ 2 = 2 x^ 3 (lnx - λ) , where λ is

NTA Abhyas JEE Main 2020 Solution View → 63

If f(x) = ((2 + x)/(1 + x)) ^ 1 + x , then f ^ ′ (0) is equal to

NTA Abhyas JEE Main 2020 Solution View → 64

If f (x) = x^ 3 + 3x + 1 and g(x) is the inverse function of f (x) , then the value of g^ ' (5) is equal to

NTA Abhyas JEE Main 2020 Solution View → 65

If y = (1)/(x) , then the value of dy 1 + y^ 4 + dx 1 + x^ 4 + 3 is equal to

NTA Abhyas JEE Main 2020 Solution View → 66

If y = ta n ^ - 1 ( x 1 + 6 x ^ 2 ) + ta n ^ - 1 ((2x - 1)/(2x + 1))(∀ x > 0) , then (dy)/(dx) is equal to

NTA Abhyas JEE Main 2020 Solution View → 67

If x = sec ⁡ t + tan ⁡ t and& y = sec ⁡ t - tan ⁡ t , where t is a parameter, then the value of (dy)/(dx) when x = 1 3 is

NTA Abhyas JEE Main 2020 Solution View → 68

If y = (1 + x)y + sin^ - 1 ( sin^ 2 x) , then (dy)/(dx) at x = 0 is

NTA Abhyas JEE Main 2020 Solution View → 69

If f ( x ) = co s ^ - 1 (sinx(4co s ^ 2 x - 1)) , then (1)/(π) f ^ ' ((π)/(3)) ⋅ f((π)/(10)) is

NTA Abhyas JEE Main 2020 Solution View → 70

If f (x) is a twice differentiable function such that f^ " (x) = - f(x) , f^ ' (x) = g (x) , h (x) = f^ 2 (x) + g^ 2 (x) and h (10) = 10, then h (5) is equal to

NTA Abhyas JEE Main 2020 Solution View → 71

Let g (x) = | x - 2| and h(x) = g (g (x)) be two functions, then the value of h^ ' (-1) + h^ ' (1)+ h^ ' (3) + h^ ' (5) is equal to (where,h^ ' denotes the derivative of h )

NTA Abhyas JEE Main 2020 Solution View → 72

If x = 3cos ⁡ t and y = 5sin ⁡ t , where t is a parameter, then 9 d ^ 2 y d x ^ 2 at t = - (π)/(6) is equal to

NTA Abhyas JEE Main 2020 Solution View → 73

If y = cos ⁡ xcos ⁡ 2xcos ⁡ 4xcos ⁡ 8x , then (dy)/(dx) at x = (π)/(2) is

NTA Abhyas JEE Main 2020 Solution View → 74

If y = |tan ⁡ x - |sin ⁡ x|| , then the value of (dy)/(dx) at x = (5π)/(4) is

NTA Abhyas JEE Main 2020 Solution View → 75

Let f(x) = x ^ 2 - 4x - 3,x > 2 and g ( x ) be the inverse of f ( x ) . Then the value of 1 g ^ ' ( 2 ) , where f ( x ) = 2 , is (here, g ^ ' represents the first derivative of g )

NTA Abhyas JEE Main 2020 Solution View → 76

If f(x) = ||2sin ⁡ x - 1| - 2cot ⁡ x| , then the value of f ^ ' ((π)/(3)) is equal to

NTA Abhyas JEE Main 2020 Solution View → 77

If f: R → R is a function defined as f( x ^ 3 ) = x ^ 5 , ∀ x ∈ R - \ 0\ and f(x) is differentiable ∀ x ∈ R , then the value of (1)/(4) f ^ ' (27) is equal to (here f ^ '

NTA Abhyas JEE Main 2020 Solution View → 78

If y = 2 + sin ⁡ x + 2 + sin ⁡ x + 2 + sin ⁡ x + … ∞ , then the value of (dy)/(dx) at x = 0 is

NTA Abhyas JEE Main 2020 Solution View → 79

Let f(x) is a differentiable function on x ∈ R , such that f(x + y) = f(x)f(y) for all x, y ∈ R where f(0) ≠ 0 . If f(5) = 10, f ^ ' (0) = 6 , then the value of f ^ ′ (5) is equal

NTA Abhyas JEE Main 2020 Solution View → 80

If f(x) = x - 4 x - 4 + ta n ^ - 1 ((1 - 2x)/(2 + x)), ∀ 4 < x < 8, then the value of f ^ ′ (5) is equal to

NTA Abhyas JEE Main 2020 Solution View → 81

If f (x) = (x – 1) (x – 2)(x – 3)(x – 4)(x – 5) , then the value of f^ &#8242; (5) is equal to

NTA Abhyas JEE Main 2020 Solution View → 82

Consider the function f(x) = ta n ^ - 1 \ (3x - 2)/(3 + 2x)\ , ∀ x ≥ 0 . If g(x) is the inverse function of f(x), then the value of g ^ ′ ((π)/(4)) is equal to

NTA Abhyas JEE Main 2020 Solution View → 83

Let f(x) = ta n ^ - 1 ( x ^ 3 - 1 x ^ 2 + x ) , then the value of 17 f ^ ′ (2) is equal to

NTA Abhyas JEE Main 2020 Solution View → 84

If I _ n = d ^ n d x ^ n ( x ^ n ln ⁡ x) , then the value of (1)/(50)( I _ 7 - 7 I _ 6 ) is equal to

NTA Abhyas JEE Main 2020 Solution View → 85

Let y = xlo g _ e x . If the value of (dy)/(dx) at x = e ^ 4 is k , then the value of 4 e ^ 3 k is (use e = 2.7 )

NTA Abhyas JEE Main 2020 Solution View → 86

If x^ y . y^ x = 16 , then the value of (dy)/(dx) at ( 2, 2 ) is

NTA Abhyas JEE Main 2020 Solution View → 87

Let f (x) be a differentiable function on x ∈ ℝ such that f (x + y) = f (x) ⋅ f(y) for all x, y . If f (0) ≠ 0, f (5) = 12 and f^ ′ (0) = 16 , then f^ ′ (5) is equal to

NTA Abhyas JEE Main 2020 Solution View → 88

If y = sin^ - 1 ( 2x 1 + x^ 2 ), then (dy)/(dx) is

NTA Abhyas JEE Main 2020 Solution View → 89

If the function f(x) = ^ - 1 ⁡ (x(3)/(2) - 1 - x - x ^ 2 + x ^ 3 ) (where, ∀ 0 < x < 1 ), then the value of | 3 f ^ ' ((1)/(2))| is equal to (take 3 = 1.73 )

NTA Abhyas JEE Main 2020 Solution View → 90

Consider a function& f (x) = x^ x , ∀ x ∈ [1, ∞). If g (x) is the inverse function of f (x) , then the value of g^ ′ (4) is equal to

NTA Abhyas JEE Main 2020 Solution View → 91

If ϕ (x) = _ 8 ⁡ _ 3 ⁡ x, then ϕ ^ ′ (e) is equal to

NTA Abhyas JEE Main 2020 Solution View → 92

If f(x) = sin ^ - 1 ( 2 × 3 ^ x 1 + 9 ^ x ), then f ^ ' (- (1)/(2)) is equal to

NTA Abhyas JEE Main 2020 Solution View → 93

The derivative of ^ - 1 ((sinx - cosx)/(sinx + cosx)) with respect to (x)/(2), where x ∈ (0, (π)/(2)) , is

JEE Main 2019 Solution View → 94

If e ^ y + xy = e, the ordered pair ((dy)/(dx), d ^ 2 y d x ^ 2 ) at x = 0 is equal to

JEE Main 2019 Solution View → 95

If f(1) = 1, f ^ ' (1) = 3 , then the derivative of f(f(f(x))) + (f(x)) ^ 2 at x = 1 is:

JEE Main 2019 Solution View → 96

If 2y = ( cot ^ - 1 ( 3 cosx + sinx cosx - 3 sinx )) ^ 2 ∀ x ∈ (0, (π)/(2)) , then (dy)/(dx) is equal to

JEE Main 2019 Solution View → 97

Let f be a differentiable function such that f(1) = 2 and f ^ ' (x) = f(x) for all x ∈ R . If h(x) = f(f(x)) , then h ^ ' (1) is equal to :

JEE Main 2019 Solution View → 98

For x > 1 , if (2x) ^ 2y = 4 e ^ 2x - 2y , then (1 + _ e ⁡ 2x) ^ 2 (dy)/(dx) is equal to

JEE Main 2019 Solution View → 99

If x _ e ( _ e x)-x^ 2 +y^ 2 =4(y>0), then (d y)/(d x) at x=e is equal to :

JEE Main 2019 Solution View → 100

Let, f: R → R be a function such that f(x) = x ^ 3 + x ^ 2 f ' (1) + xf '' (2) + f ''' (3), ∀ x ∈ R . Then f(2) equals

JEE Main 2019 Solution View → 101

If x = 3tant and y = 3sect, then the value of d ^ 2 y d x ^ 2 at t = (π)/(4), is:

JEE Main 2019 Solution View → 102

If x = 2 ^ cosec ^ - 1 t and y = 2 ^ sec ^ - 1 t , (|t| ≥ 1), then (dy)/(dx) is equal to

JEE Main 2018 Solution View → 103

If f(x)= ^ -1 ((2 × 3^x)/(1+9^x)) , then f^ (-(1)/(2)) equals.

JEE Main 2018 Solution View → 104

If x^2+y^2+ y=4 , then the value of (d^2 y)/(d x^2) at the point (-2,0) is

JEE Main 2018 Solution View → 105

If x ^ 2 + y ^ 2 + siny = 4 , then the value of d ^ 2 y d x ^ 2 at the point (- 2, 0) is :

JEE Main 2018 Solution View → 106

If 2x = y ^ (1)/(5) + y ^ - (1)/(5) and ( x ^ 2 - 1) d ^ 2 y d x ^ 2 + (dy)/(dx) + ky = 0 , then λ + k is equal to

JEE Main 2017 Solution View → 107

If y = [x + x ^ 2 - 1 ] ^ 15 + [x - x ^ 2 - 1 ] ^ 15 , then ( x ^ 2 - 1) d ^ 2 y d x ^ 2 + x(dy)/(dx) is equal to

JEE Main 2017 Solution View → 108

If for x ∈ (0, (1)/(4)), the derivative of ^ - 1 ⁡ ( 6x x 1 - 9 x ^ 3 ) is x ⋅ g(x) , then g(x) equals:

JEE Main 2017 Solution View → 109

Let f: R → R, g: R → R and h: R → R be differentiable functions such that f(x) = x ^ 3 + 3x + 2, g(f(x)) = x and h(g(g(x))) = x , for all x ∈ R . Then,

JEE Advanced 2016 Solution View → 110

Let f and g be two differentiable functions on R such that f^ (x)>0 and g^ (x) < 0 for all x ∈ R . Then for all x :

JEE Main 2014 Solution View → 111

If y = e ^ nx , then d ^ 2 y d x ^ 2 . d ^ 2 x d y ^ 2 is equal to :

JEE Main 2014 Solution View → 112

Let f ⁡ (x) = x π x , x > 0 . Then for all natural numbers n , f ⁡ ^ ′ (x) vanishes at

JEE Advanced 2013 Solution View → 113

If f(x)= ( x) and f^ (x)+ x f^ (x)+g(x) =0 , then g(x) is :

JEE Main 2013 Solution View → 114

For a>0, t ∈(0, (π)/(2)) , let x= a^ ^ -1 t and y= a^ ^ -1 t , Then, 1+((d y)/(d x))^2 equals :

JEE Main 2013 Solution View → 115

Let f(x)=(x^2-x)/(x^2+2 x) x ≠ 0,-2 . Then (d)/(d x)[f^ -1 (x)] (wherever it is defined) is equal to:

JEE Main 2013 Solution View → 116

If y = sec( ^ - 1 x) , then (dy)/(dx) at x = 1 is equal to

JEE Main 2013 Solution View → 117

If f^ (x)= ( x) and y=f((2 x+3)/(3-2 x)) , then (d y)/(d x) equals

JEE Main 2012 Solution View → 118

(d^2 x)/(d y^2) equals

JEE Main 2011 Solution View → 119

Let f be a real-valued function defined on the interval (-1,1) such that e^ -x f(x)=2+∫_0^x t^4+1 d t, for all x ∈(-1,1) and let f^ -1 be the inverse function of f . Then (f^ -1

JEE Advanced 2010 Solution View → 120

Let f:(-1,1) arrow R be a differentiable function with f(0)=-1 and f^ (0)=1 . Let g(x)=[f(2 f(x)+2)]^2 . Then g^ (0)=

JEE Main 2010 Solution View → 121

If the function f(x)=x^3+e^ (x)/(2) and g(x)=f^ -1 (x) , then the value of g^ (1) is

JEE Advanced 2009 Solution View → 122

Let y be an implicit function of x defined by x^ 2 x -2 x^x y-1=0 . Then y^ (1) equals

JEE Main 2009 Solution View → 123

Paragraph: Consider the function f:(-∞, ∞) arrow(-∞, ∞) defined by f(x)=(x^2-a x+1)/(x^2+a x+1) ; 0 Question: Which of the following is true ?

JEE Advanced 2008 Solution View → 124

Paragraph: Consider the functions defined implicitly by the equation y^3-3 y+x=0 on various intervals in the real line. If x ∈(-∞,-2) ∪(2, ∞) , the equation implicitly defines a

JEE Advanced 2008 Solution View → 125

(d^2 x)/(d y^2) equals

JEE Advanced 2007 Solution View → 126

If f^ (x)=-f(x) , where f(x) is a continuous double differentiable function and g(x)=f^ (x) . If F(x)=(f((x)/(2)))^2+(g((x)/(2)))^2 and F(5)=5 , then F(10) is

JEE Advanced 2006 Solution View → 127

If x^m · y^n=(x+y)^ m+n , then (d y)/(d x) is

JEE Main 2006 Solution View → 128

Suppose f(x) is differentiable x=1 and _ h arrow 0 (1)/(h) f(1+h)=5 , then f^ (1) equals

JEE Main 2005 Solution View → 129

If x=e^ y+e^ y+. .10 ∞ , x>0 , then (d y)/(d x) is

JEE Main 2004 Solution View → 130

If y=(x+ 1+x^2 )^n, then (1+x^2) (d^2 y)/(d x^2) + x (d y)/(d x) i s

JEE Main 2002 Solution View → 131

If h(x)=x^ x^x , then at x=1, h^ (x) h(x) is equal to

99 Percentile Qs Bank for JEE Main Solution View → 132

If y=A n x+B n x , then y_2+n^2 y is equal to

99 Percentile Qs Bank for JEE Main Solution View → 133

If u=x y^2 ^ -1 \ left((y)/(x)), then x (∂ u)/(∂ x)+ y (∂ u)/(∂ y) is equal to

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If f(x)= a x + a^2 a x , then f^ (a) is equal to

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If u(x, y)=y x+x y , then u_x u_y-u_x x-u_y y+ x y is equal to :

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(d)/(d x) ^ -1 (3 x-4 x^3) is equal to

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If y=a x+(5+2 x) x , then y^ +y=

99 Percentile Qs Bank for JEE Main Solution View → 138

If f(x) = | cases x & x^ 2 & x^ 3 1 & 2x & 3x^ 2 0 & 2 & 6x cases | , then the ratio f^ '' ( x ) : f^ ' ( x ) =

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(d)/(d x)((x+5)/((x+1)^2(x+2)))=

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If y=( ^ -1 2 x)^2+( ^ -1 2 x)^2 , then (1-4 x^2) y_2-4 x y_1=

99 Percentile Qs Bank for JEE Main Solution View → 141

If y=2 (2 x)+3 (2 x) , then x^2 y^ +x y^ +2 y=

99 Percentile Qs Bank for JEE Main Solution View → 142

If z=(y)/(x) [ (x)/(y)+ (1+(y)/(x))], then x (∂ z)/(∂ x) is equal to

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If y= x+ y+ x+ y+… ∞ , then (d y)/(d x)=

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y= [3] 1+3 x [4] 1+4 x [5] 1+5 x [7] 1+7 x [8] 1+8 x . Then d y ~d x at x=0 is

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If a x^2+2 h x y+b y^2=3 , then (d^2 y)/(d x^2)=

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If y^ x =x^ y , then (d y)/(d x)=

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If x=a\ θ+ ((θ)/(2))\ and y=a θ , then (d y)/(d x) is equal to

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If y^ 2 =a x^ 2 +b x+c, where a, b, c are constants, then y^ 3 d^ 2 y d x^ 2 is equal to

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If x= 1-t^ 2 1+t^ 2 and y= 2 a t 1+t^ 2 , then (d y)/(d x) is equal to

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If y=x^ n x+x( x)^ n , then (d y)/(d x) is equal to

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The valuc of f(4)-f(3) is

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The derivative of f( x) w.r.t. g( x) at x=(π)/(4) , where f^ (1)=2 and g^ ( 2 )=4 is

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If y= ^ -1 \ left[ x- 1-x^ 2 x+ 1-x^ 2 ], then \ left((d y)/(d x))=

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Let ϕ ( x ) be the inverse of the function f ( x ) and f^ ′ (x) = 1 1 + x^ 5 ,then (d)/(dx) ϕ(x) is equal to

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If y = ^ - 1 (secx - tanx), then the absolute value of 2 (dy)/(dx) is

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Let y = x^ x^ x … ∞ , then (dy)/(dx) is equal to (given x > 0 )

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If x = 1 - t^ 2 1 + t^ 2 and y = 2t 1 + t^ 2 , then(dy)/(dx) is equal to

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If & ( cos&thinsp;x ) ^ y = ( siny ) ^ x , &thinsp;find&thinsp;(dy)/(dx) .

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If& f ( x ) has a derivative at~ x = a, then _ x → a (xf(a) - af(x))/(x - a) is equal to

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If y = ^ - 1 ((sinx + cosx)/(cosx - sinx)), ~then (dy)/(dx) is equal to

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If f(x)=∏_ n=1 ^ 50 (x-n)^ n(51-n) ; then f(51) f^ (51)

Most Important Selected Qs for JEE Advanced Solution View → 162

If y= ( ^ -1 x) , then (d y)/(d x) at x=1 is equal to:

Most Important Selected Qs for JEE Advanced Solution View → 163

STATEMENT 1: If y= (m ^ -1 x) then (1-x²) y_ n+2 -(2 n+1) x y_ n+1 +(n²-m²) y_n=0 [ y_n is n th derivative of y w.r.t. x ] STATEMENT 2: (d^n)/(d x^n)[ u(x) v(x)]=u_n v_0+ ^n C_1

Most Important Selected Qs for JEE Advanced Solution View → 164

Match the following List-I with List-II

Most Important Selected Qs for JEE Advanced Solution View → 165

If y= a^2-b^2 ^2( x) then x^2 y^2((d y)/(d x))^2 is equal to

Most Important Selected Qs for JEE Advanced Solution View → 166

If f(x)=∏_ n=1 ^ 50 (x-n)^ n(51-n) ; then f(51) f^ (51)

Most Important Selected Qs for JEE Advanced Solution View → 167

STATEMENT 1: If y= (m ^ -1 x) then (1-x²) y_ n+2 -(2 n+1) x y_ n+1 +(n²-m²) y_n=0 [ y_n is n th derivative of y w.r.t. x ] STATEMENT 2: (d^n)/(d x^n)[ u(x) v(x)]=u_n v_0+ ^n C_1

Most Important Selected Qs for JEE Advanced Solution View → 168

If y= ( ^ -1 x) , then (d y)/(d x) at x=1 is equal to:

Most Important Selected Qs for JEE Advanced Solution View → 169

If y= a^2-b^2 ^2( x) then x^2 y^2((d y)/(d x))^2 is equal to

Most Important Selected Qs for JEE Advanced Solution View → 170

Match the following List-I with List-II

Most Important Selected Qs for JEE Advanced Solution View → 171

Consider a cubic, f(x)=a x^3+b x^2+c x+4, a, b, c ∈ R and f^ ((-2)/(3))=0, f^ (0)=3 , f^ ((-2)/(3))=(5)/(3) , and g=f^ -1 , then:

Most Important Selected Qs for JEE Advanced Solution View → 172

If y= x+ x+ x+ x+… … , where x>0 , then (d y)/(d x) can be:

Most Important Selected Qs for JEE Advanced Solution View → 173

Let f: R arrow R be defined as f(x)=(2 x-3 π)^3+(4 x)/(3)+ x and g=f^ -1 , then find the value of 7 g^ (2 π)+3 g^ (2 π) .

Most Important Selected Qs for JEE Advanced Solution View → 174

If f(x)=(x-1)^ 100 (x-2)^ 2(99) (x-3)^ 3(98) … . .(x-n)^ 100 , let k= f^ (101) f(101) , then ((k)/(50)-97) is ______

Most Important Selected Qs for JEE Advanced Solution View → 175

Let f: R arrow R be a function defined by f(x)=x^3+2 x^2+3 x+2 and g be the inverse function of f . If .(d)/(d x)(g(g(g(x))))|_ x=24 =(p)/(q) , where p, q are co-prime, then find

Most Important Selected Qs for JEE Advanced Solution View → 176

If x=4 t^3+3, y=4+3 t^4 and (((d^2 x)/(d y^2)))/(((d x)/(d y))^n) is a constant, then find the value of (4)/(5)+(4)/(5 n)+(4)/(5 n^2)+… . . upto infinity.

Most Important Selected Qs for JEE Advanced Solution View → 177

If x ∫_0^x (f(t)) d t=(x+2) ∫_0^x t (f(t)) d t where x>0 , then find the value of f^ (x) (f(x))+(3)/(1+x)

Most Important Selected Qs for JEE Advanced Solution View → 178

If y = 10 ( ^ -1 ( 1+x^2 -1 x ))^2 , where x ≠ 0 , then the value of (1+x^2)^2 y'' + 2x(1+x^2)y' is

JEE Main Solution View → 179

Let A(x) = pmatrix f(x) & g(x) -g(x) & f(x) pmatrix be a matrix defined for all real x , where f(x) and g(x) are differentiable functions. If A(x+y) = A(x)A(y) for all x, y ∈ ℝ

JEE Main Solution View → 180

Let P(x) be a polynomial of degree 3 such that it satisfies the identity P(x) + P'(x) + P''(x) = x^3 + 5x^2 + 13x + 11 for all real x . The value of P(2) is equal to:

JEE Main Solution View → 181

Let f(x) and g(x) be polynomials defined as f(x) = x^2 + x g'(1) + g''(2) and g(x) = x^3 + x^2 f'(1) + x f''(2) for all x ∈ ℝ . The value of f(10) + g(10) is equal to

JEE Main Solution View → 182

Let f : ℝ → ℝ be a differentiable function satisfying f(x+y) = f(x) + f(y) + 3x^2y + 3xy^2 for all x, y ∈ ℝ . If _ x → 0 (f(x))/(x) = 1 and g(x) is the inverse function of f(x)

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Let y = ^ -1 ((1-x^2)/(1+x^2)) - ^ -1 ((2x)/(1+x^2)) . The set of all values of x for which (dy)/(dx) = 0 is

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Let f: R arrow R be a twice differentiable function satisfying the determinant equation vmatrix f(x+y) & 2x + 2y f(x-y) & 2x - 2y vmatrix = 0 for all x, y ∈ R . If f'(0) = 4

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Let f(x) and g(x) be twice differentiable functions on R satisfying f''(x) - g''(x) = 24x . If the function f(x) - g(x) has a local minimum at x = 1 with a minimum value of -3

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Let f(x) be a bijective differentiable function and h(x) be its inverse function. It is given that f(1) = 2 , f(3) = 9 , f^ (1) = 3 , and f^ (3) = (1)/(2) . If a function g(x) is

JEE Main Solution View → 187

Let f(x) and g(x) be twice differentiable functions satisfying f''(x) - g''(x) = 2 for all x ∈ R . If the tangent to the curve y = f(x) - g(x) at x = 3 is given by the equation y

JEE Main Solution View → 188

Let f(x) = x^3 + vmatrix x^2 & x & 1 f'(1) & f''(2) & f'''(3) 1 & 1 & 0 vmatrix , \ x ∈ ℝ . Then the value of f(10) is equal to

JEE Main Solution View → 189

Let f be a differentiable function such that f(0) = 0 , f(1) = 3 , and f^ (0) = 4 . A new function g is defined as g(x) = f(2x+1) · e^ 2f(x) . If g^ (0) = 40 , then the value of

JEE Main Solution View → 190

A cubic polynomial curve y = f(x) = ax^3 + bx^2 + cx + d has a point of inflection at x = 1 and passes through the point (1, 1) . If the tangent to the curve at the point (0, 2)

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Related JEE Mathematics chapters

Application of Derivatives (795)Three Dimensional Geometry (756)Sequences and Series (748)Functions (700)Definite Integration (692)Vector Algebra (616)Differential Equations (586)Continuity and Differentiability (576)Probability (561)Complex Number (551)Binomial Theorem (550)Quadratic Equation (517)

Differentiation in other exams

NDA Differentiation (104)BITSAT Differentiation (20)