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NDA Differentiation PYQs with Solutions

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

104 questionsMathematics2010–2026Answers + solutions

About Differentiation PYQs

Differentiation has 104 previous year questions in the Quantrex Academy NDA Mathematics bank. The 104 questions in this list come from NDA (104), spanning 2010 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

NDA Differentiation PYQs with Solutions

About Differentiation PYQs

Questions by year (this list)

Differentiation questions with solutions

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=y_0 when x=1 ?

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

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 ?

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

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

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

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

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

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?

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?

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

Paragraph: Let f:(-1,1) arrow 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?

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?

Paragraph: Let f:(-1,1) arrow 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 ^ (0) equal to?

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?

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

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

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

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

What is the derivative of cosec (x^ ^ ∘ ) ?

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

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

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

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

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

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?

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

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

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

If y=(1+x) (1+x^2) (1+x⁴)(1+x⁸)(1+x^ 16 ) then what is (d y)/(d x) at x=0 equal to?

If y= x · 4 x · 8 x , then what is (1)/(y) (d y)/(d x) at x=(π)/(4) equal to?

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

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

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

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

What is the derivative of ^ -1 x with respect to ^ -1 x ?

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

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

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

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

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

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

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) ?

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

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

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

What is d 1- 2 x dx equal to, where (π)/(4) < x < (π)/(2) ?

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

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

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

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

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

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?

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

If l_1= d dx ( ^ x ) aligned & l_2= _ h arrow 0 ^ (x+h) - ^ x h & l_3=∫ ^ x xdx aligned then which one of the following is correct?

What is (d^2 x)/(d y^2) equal to?

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) ]?

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

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 ?

Let f: R arrow 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 ^ (1) equal to?

Let f: R arrow 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?

Let f: R arrow 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

Let f: R arrow 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?

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

If f(x)= 25-x^2 , then what is Lim_ x arrow 1 (f(x)-f(1))/(x-1) equal to ?

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

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

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

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

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

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?

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

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

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?

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

What is the derivative of (1+ x)/(1- x) ?