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Differentiation — NDA Mathematics PYQs

104 previous year questions from Differentiation with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

104 questionsMathematicsSolutions on every page
1

Passage: Let (e^y )^x-y=0 , where y is a function of x whose domain is (0,10] . Question: What is dy dx equal to, given that y=y₀ when x=1 ?

NDA 2026 Solution View → 2

If [4] y =x+ x^2+4 , then what is x^2+4 , dy dx equal to ?

NDA 2026 Solution View → 3

Passage: Let (e^y )^x-y=0 , where y is a function of x whose domain is (0,10] . Question: What is dy dx equal to ?

NDA 2026 Solution View → 4

For the following two (02) items: Consider the function f(x) = cases 4(5^x), & x What is f'(-1) equal to?

NDA 2025 Solution View → 5

Consider the following for the two (02) items that follow: Let x = - and y = ^4 - ^4 . What is ( dy dx )^2 equal to?

NDA 2025 Solution View → 6

Consider the following for the two (02) items that follow: Let (x+y)^ p+q = x^p y^q , where p , q are positive integers. The derivative of y with respect to x

NDA 2025 Solution View → 7

Consider the following for the two (02) items that follow: Let y = ⁻¹ (x - 4x^3 27 ) . What is dy dx equal to?

NDA 2025 Solution View → 8

For the following three (03) items: Let y = f(x) = x ⁻¹ x 1 - x^2 + 1 - x^2 . If x = , then what is dy dx equal to?

NDA 2025 Solution View → 9

Consider the following for the two (02) items that follow: Let (x+y)^ p+q = x^p y^q , where p , q are positive integers. If p + q = 10 , then what is dy dx equal to?

NDA 2025 Solution View → 10

For the following three (03) items: Let y = f(x) = x ⁻¹ x 1 - x^2 + 1 - x^2 . What is d^2y dx^2 at x = 0 equal to?

NDA 2025 Solution View → 11

Consider the following for the two (02) items that follow: Let x = - and y = ^4 - ^4 . What is ( x^2+4 y^2+4 ) dy dx [(x^2+4) d^2y dx^2 - 16y ] equal to?

NDA 2025 Solution View → 12

Paragraph: Let f:(-1,1) R be a differentiable function with f(0)=-1 and f^ (0)=1 . Let h(x)=f(2 f(x)+2) and g(x)=(h(x))^2 . Question: What is g^ (0) equal to?

NDA 2024 Solution View → 13

Let f(x) and g(x) be two functions such that g(x)=x- 1 x and f o g(x)=x^3- 1 x^3 . What is f^ (x) equal to?

NDA 2024 Solution View → 14

Paragraph: Let f:(-1,1) R be a differentiable function with f(0)=-1 and f^ (0)=1 . Let h(x)=f(2 f(x)+2) and g(x)=(h(x))^2 . Question: What is h ^ (0) equal to?

NDA 2024 Solution View → 15

Let a function f be defined on R - 0 and 2 f(x)+f ( 1 x )=x+3 If f is differentiable, then what is (0.5) equal to?

NDA 2023 Solution View → 16

If f(x)=| | x| | where 0 x 1 , then what is f^ (0.5) equal to?

NDA 2023 Solution View → 17

If f^ (x)= ( x) and y f ( array ll 2 & 3 array ) , then what is d y d x equal to?

NDA 2023 Solution View → 18

Paragraph: Let f(x)=| x|, x 1 Question: What is the derivative of f(x) at x=2 ?

NDA 2023 Solution View → 19

Paragraph: Let f(x)=| x|, x 1 Question: What is the derivative of f f(x) , where 1 x 2 ?

NDA 2023 Solution View → 20

What is the derivative of cosec (x^ ) ?

NDA 2023 Solution View → 21

What is the derivative of ^2 x with respect to ^2 x ?

NDA 2023 Solution View → 22

Paragraph: Let f(x)=| x|, x 1 Question: What is the derivative of f(x) at x=0.5 ?

NDA 2023 Solution View → 23

If y= x x^2-16 2 -8 |x+ x^2-16 | , then what is d y d x equal to?

NDA 2022 Solution View → 24

If y= (x^ x )^ x then which one of the following is correct?

NDA 2022 Solution View → 25

In y= ^2 ( x^2-x+1 x^2+x+1 ) , then what is d y d x at x=0 equal to?

NDA 2022 Solution View → 26

If d d x ( 1+x^4+x^8 1-x^2+x^4 )=a x+b x^3 , then which one of the following is correct?

NDA 2022 Solution View → 27

If x^y y^x=1 , then what is d y d x at (1,1) equal to?

NDA 2022 Solution View → 28

If y= (x^x )^x , then what is the value of d y d x at x=1 ?

NDA 2022 Solution View → 29

What is the derivative of e^ e^x with respect to e^x ?

NDA 2021 Solution View → 30

If y=(1+x) (1+x^2 ) (1+x^4 ) (1+x^8 ) (1+x¹⁶ ) then what is d y d x at x=0 equal to?

NDA 2021 Solution View → 31

If y= x 4 x 8 x , then what is 1 y d y d x at x= 4 equal to?

NDA 2021 Solution View → 32

Let f(x) be a polynomial function such that f f(x)=x^4 . What is f^ (1) equal to?

NDA 2021 Solution View → 33

What is the derivative of ( x)+ ( x) with respect to x at x=e ?

NDA 2021 Solution View → 34

What is the derivative of e^x with respect to x^e ?

NDA 2021 Solution View → 35

If x=e^t t and y=e^t t , then what is d x d y at t=0 equal to?

NDA 2021 Solution View → 36

What is the derivative of ⁻¹ x with respect to ⁻¹ x ?

NDA 2020 Solution View → 37

If e^ =c+4 , where c is an arbitrary constant and is a function of , then what is d equal to?

NDA 2020 Solution View → 38

If x^m y^n=a^ m+n , then what is d y d x equal to?

NDA 2020 Solution View → 39

Paragraph: Consider the equation x^y=e^ x-y Question: What is d y d x at x=1 equal to ?

NDA 2019 Solution View → 40

What is the derivative of ^2 ( ⁻¹ x ) with respect to x ?

NDA 2019 Solution View → 41

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

NDA 2019 Solution View → 42

Paragraph: Consider the equation x^y=e^ x-y Question: What is d^2 y d x^2 at x=1 equal to?

NDA 2019 Solution View → 43

Paragraph: Let f(x)=x^2+2 x-5 and g(x)=5 x+30 Question: If h(x)=5 f(x)-x g(x) , then what is the derivative of h(x) ?

NDA 2019 Solution View → 44

What is the derivative of 2^ ( x)^2 with respect to x ?

NDA 2019 Solution View → 45

If y=a 2 x+b 2 x , then

NDA 2019 Solution View → 46

If y= ⁻¹ ( 5-2 x 2+5 x ) , then what is d y d x equal to?

NDA 2018 Solution View → 47

What is d 1- 2 x dx equal to, where 4 x 2 ?

NDA 2018 Solution View → 48

What is the derivative of the function f ( x )= e ^ x + ( x )- e ^ x at x = 4 ?

NDA 2018 Solution View → 49

If f(x) is an even function, where f(x) 0 , then which one of the following is correct?

NDA 2018 Solution View → 50

If y = e ^ x ^2 2 x , then what is dy dx at x = equal to?

NDA 2018 Solution View → 51

If y=| x|^ |x| , then what is the value of d y d x at x= 6 ?

NDA 2018 Solution View → 52

If y= ( x) , then which one of the following is correct?

NDA 2018 Solution View → 53

If u=e^ a x b x and v=e^ a x b x , then what is u d u d x +v d v d x equal to?

NDA 2018 Solution View → 54

If y =( x )^ ( x )^ ( x)^ x , then dy dx is equal to

NDA 2017 Solution View → 55

If l₁= d dx ( e ^ x ) aligned & l₂= _ h 0 e ^ ( x + h ) - e ^ x h & l₃= e ^ x xdx aligned then which one of the following is correct?

NDA 2017 Solution View → 56

What is d^2 x d y^2 equal to?

NDA 2017 Solution View → 57

Let f( x + y )=f( x ) f( y ) for all x and y . Then what is f^ (5) equal to [where f^ ( x ) is the derivative of f( x ) ]?

NDA 2017 Solution View → 58

What is the derivative of ₁₀ (5 x ^2+3 ) with respect to x ?

NDA 2017 Solution View → 59

Consider the equation x+|y|=2 y . What is the derivative of y as a function of x with respect to x for x 0 ?

NDA 2016 Solution View → 60

Let f : R R be a function such that f(x)=x^3+x^2 f^ (1)+x f f^ (2)+f^ (3) for x R What is f ^ (1) equal to?

NDA 2016 Solution View → 61

Let f : R R be a function such that f(x)=x^3+x^2 f^ (1)+x f f^ (2)+f^ (3) for x R What is f (1) equal to?

NDA 2016 Solution View → 62

Let f : R R be a function such that f(x)=x^3+x^2 f^ (1)+x f f^ (2)+f^ (3) for x R Consider the following: 1. f (2)= f (1)- f (0) 2. f^ (2)-2 f^ (1)=12 Which of the above is/are cor

NDA 2016 Solution View → 63

Let f : R R be a function such that f(x)=x^3+x^2 f^ (1)+x f f^ (2)+f^ (3) for x R What is f "'(10) equal to?

NDA 2016 Solution View → 64

Consider the function f ( x )= | x ^2-5 x +6 | What is f "(2.5) equal to?

NDA 2016 Solution View → 65

If f(x)= 25-x^2 , then what is Lim _ x 1 f(x)-f(1) x-1 equal to ?

NDA 2015 Solution View → 66

The derivative of (x+ x) with respect to (x+ x) is

NDA 2015 Solution View → 67

If x^a y^b=(x-y)^ a+b , then the value of d y d x - y x is equal to

NDA 2015 Solution View → 68

If s = t ^2+1 , then d ^2 ~s dt ^2 is equal to

NDA 2015 Solution View → 69

Consider f ^ ( x )= x ^2 2 - kx +1 such that f (0)=0 and f (3)=15 f ^ (- 2 3 ) is equal to

NDA 2015 Solution View → 70

Given that d d x ( 1+x^2+x^4 1+x+x^2 )=A x+B What is the value of A?

NDA 2015 Solution View → 71

Consider the parametric equation x= a (1-t^2 ) 1+t^2 , y= 2 a t 1+t^2 What is d y d x equal to?

NDA 2015 Solution View → 72

Given that d d x ( 1+x^2+x^4 1+x+x^2 )=A x+B What is the value of B?

NDA 2015 Solution View → 73

What is the derivative of ⁻¹ ( 1+x^2 -1 x ) with respect to ⁻¹ x ?

NDA 2015 Solution View → 74

Consider the parametric equation x= a (1-t^2 ) 1+t^2 , y= 2 a t 1+t^2 What is d^2 y d x^2 equal to?

NDA 2015 Solution View → 75

Consider the curve x=a( + ) and y=a( - ) . What is d y d x equal to?

NDA 2014 Solution View → 76

What is the derivative of 1+ x 1- x ?

NDA 2014 Solution View → 77

If y=x x+x e^x , then what is the value of d y d x at x=1 ?

NDA 2014 Solution View → 78

Consider the curve x=a( + ) and y=a( - ) . What is d^2 y d x^2 equal to?

NDA 2014 Solution View → 79

If z=fof(x) where f(x)=x^2 , then what is d z d x equal to?

NDA 2014 Solution View → 80

What is the derivative of |x-1| at x=2 ?

NDA 2013 Solution View → 81

If f(x)=2 x^2+3 x-5 , then what is f^ (0)+3 f^ (-1) equal to?

NDA 2013 Solution View → 82

What is the derivative of x^3 with respect to x^2 ?

NDA 2013 Solution View → 83

If 2 x^3-3 y^2=7 , what is d y d x equal to (y 0) ?

NDA 2013 Solution View → 84

What is the differential coefficient of _x x ?

NDA 2013 Solution View → 85

If y= (a x+b) , then what is d^2 y d x^2 at x=- b a , where a, b are constants and a 0 ?

NDA 2013 Solution View → 86

The derivative of ^2 x with respect to ^2 x is

NDA 2013 Solution View → 87

What is the derivative of ( x) ?

NDA 2013 Solution View → 88

If y=x^x , what is d y d x at x=1 equal to ?

NDA 2013 Solution View → 89

If x^m+y^m=1 such that d y d x =- x y , then what should be the value of m ?

NDA 2012 Solution View → 90

Consider the following statements : 1. If y= ( x+ x) , then d y d x = x . 2. If y= ( cosec x- x) , then d y d x = cosec x . Which of the above is/are correct?

NDA 2012 Solution View → 91

If y= (e^ m x +e^ -m x ) , then what is d y d x at x=0 equal to?

NDA 2012 Solution View → 92

If f(x)=2^ x , then what is the derivative of f(x) ?

NDA 2012 Solution View → 93

If y= t and x= t , then what is d y d x equal to?

NDA 2012 Solution View → 94

If y= x+1 x-1 , then what is d y d x equal to?

NDA 2012 Solution View → 95

If y= (1+x^ 1 4 ) (1+x^ 1 2 ) (1-x^ 1 4 ) , then what is d y d x equal to?

NDA 2011 Solution View → 96

If y= x , then what is the value of d y d x at x= 4 ?

NDA 2011 Solution View → 97

If f(x)=2^x , then what is f^ (x) equal to?

NDA 2011 Solution View → 98

If x + y =2 , then what is d y d x at y=1 equal to?

NDA 2010 Solution View → 99

If x=k( + ) and y=k(1+ ) , then what is the derivative of y with respect to x at = / 2 ?

NDA 2010 Solution View → 100

What is the derivative of ^2 x with respect to ^2 x ?

NDA 2010 Solution View → 101

If x= (2 t) and y= ^2 t , then what is d^2 y d x^2 equal to?

NDA 2010 Solution View → 102

If x=t^2, y=t^3 , then what is d^2 y d x^2 equal to?

NDA 2010 Solution View → 103

What is the differentiation of _x x with respect to x ?

NDA 2010 Solution View → 104

What is the derivative of x a^2-x^2 +a^2 ⁻¹ ( x a ) ?

NDA 2010 Solution View →
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