Differentiation — JEE Main PYQs & Practice Questions

Differentiation is a Mathematics chapter in the JEE Main syllabus. This page brings together 38 previous-year and practice questions on Differentiation, organised into 6 topics: Derivatives of Standard Functions, Chain Rule, Implicit Differentiation, Product and Quotient Rule, Parametric Differentiation and Higher Order Derivatives. Most questions come with a step-by-step solution you can work through free in PrepWiser.

Download Differentiation JEE Main PYQs as a free PDF (with answer key)

Revise this chapter: Revision notes · Formula sheet

Chapter weightage: how many questions each chapter had per shift in the 2024–26 papers.

Derivatives of Standard Functions

• Suppose f(x)=((2ˣ+2⁻ˣ) tan x √(tan ⁻¹(x²-x+1)))/(7 x²+3 x+1)³. Then the value of f′(0)…
• Let for a differentiable function f:(0, ∞) → R, f(x)-f(y) ≥ log ₑ(x/y)+x-y, ∀ x, y ∈(0…
• If y( α ) = √(2( (tan α + cot α)/(1 + tan ²α) ) + 1/(sin ²α)) ,α ∈ ( 3π/4,π ) dy/dα at α…

Chain Rule

• The derivative of tan ⁻¹( (√(1 + x²) - 1)/x ) with respect to tan ⁻¹( 2x√(1 - x²)/(1 -…
• Let ƒ and g be differentiable functions on R such that fog is the identity function. If…
• The value of log ₑ 2 d/(d x)(log _(cos x) cosec x) at x=π/4 is
• If f(x) = sin ( cos ⁻¹( (1 - 2²ˣ)/(1 + 2²ˣ) ) ) and its first derivative with respect to…
• If y=(√x+1)(x²-√x)/(x √x+x+√x)+1/15(3 cos ² x-5) cos ³ x, then 96 y′(π/6) is equal to :
• Let y=log ₑ((1-x²)/(1+x²)),-1 < x<1 . Then at x=1/2 , the value of 225(y′-y^(′ ′)) is…
• Let y=f(x)=sin ³(π/3(cos (π/(3 √2)(-4 x³+5 x²+1)^(3/2)))). Then, at x = 1,

Implicit Differentiation

• If y² + logₑ (cos²x) = y, x ∈ ( - π/2,π/2 ), then :
• If 2 xʸ+3 yˣ=20, then (d y)/(d x) at (2,2) is equal to :
• Let xᵏ + yᵏ = aᵏ, (a, k > 0 ) and dy/dx + ( y/x )^(1/3) = 0, then k is:
• Let y = y(x) be a function of x satisfying y√(1 - x²) = k - x√(1 - y²) where k is a…
• For the curve C:(x²+y²-3)+(x²-y²-1)⁵=0, the value of 3 y′-y³ y^(′ ′), at the point (α…
• If y = y(x) is an implicit function of x such that logₑ(x + y) = 4xy, then d²y/dx² at x…
• Let f:( 0,∞ ) → ( 0,∞ ) be a differentiable function such that f(1) = e and lim _(t → x)…
• If ( a + √2 b cos x )( a - √2 b cos y ) = a² - b² where a > b > 0, then dx/dy at(…

Product and Quotient Rule

• Suppose for a differentiable function h, h(0)=0, h(1)=1 and h′(0)=h′(1)=2. If g(x)=h(eˣ)…

Parametric Differentiation

• If the angle made by the tangent at the point (x₀, y₀) on the curve x = 12(t + sin t cos…
• If x = 2 sin θ - sin 2θ and y = 2 cos θ - cos 2θ, θ ∈ [ 0,2π ], then d²y/dx² at θ = π is :
• Let x(t)=2 √2 cos t √(sin 2 t) and y(t)=2 √2 sin t √(sin 2 t), t ∈(0, π/2). Then (1+((d…

Higher Order Derivatives

• Let f(x)=x³+x²f'(1)+2xf''(2)+f'''(3), x∈ ℝ. Then the value of f'(5) is :
• Let f(x)=a x³+b x²+c x+41 be such that f(1)=40, f′(1)=2 and f^(′ ′)(1)=4. Then a²+b²+c²…
• Let y(x) = (1 + x)(1 + x²)(1 + x⁴)(1 + x⁸)(1 + x¹⁶). Then y' - y'' at x = - 1 is equal to
• If f(x)={x³ sin (1/x),, x ≠ 0; 0, , x=0 , then
• If y(x)=xˣ,x > 0, then y''(2)-2y'(2) is equal to
• Let f(x) and g(x) be twice differentiable functions satisfying f^('')(x)=g^('')(x) for…
• If f(x) = x³ - x²f'(1) + xf''(2) - f'''(3),x ∈ ℝ, then
• Let f(x)=x³+x² f′(1)+x f^(′ ′)(2)+f^(′ ′ ′)(3), x ∈ R. Then f′(10) is equal to…
• If f(x)=x²+g′(1) x+g^(′ ′)(2) and g(x)=f(1) x²+x f′(x)+f^(′ ′)(x), then the value of…
• Let f : S → S where S = (0, ∞) be a twice differentiable function such that f(x + 1) =…
• If log ₑ y=3 sin ⁻¹ x, then (1-x²) y^(′ ′)-x y′ at x=1/2 is equal to
• If y(θ)=(2 cos θ+cos 2 θ)/(cos 3 θ+4 cos 2 θ+5 cos θ+2), then at θ=π/2, y^(′ ′)+y′+y is…
• If y^(1/4) + y^(- 1/4) = 2x, and (x² - 1)d²y/dx² + α xdy/dx + β y = 0, then | α - β | is…
• If y(x) = ( xˣ )ˣ, x > 0, then d²x/dy² + 20 at x = 1 is equal to ____________.
• If y=tan⁻¹((3 cos x-4 sin x)/(4 cos x+3 sin x))+2 tan⁻¹(x/(1+√(1-x²))), then dy/dx at…
• Let f(x)=(sin x+cos x-√2)/(sin x-cos x), x ∈[0, π]-{π/4}. Then f((7 π)/12) f^(′ ′)((7…

More Mathematics chapters

• Sets
• Relations & Functions (Basic)
• Trigonometric Ratios & Identities
• Trigonometric Equations
• Inverse Trigonometric Functions
• Properties of Triangles
• Complex Numbers
• Quadratic Equations & Polynomial Inequalities
• Sequences & Series
• Binomial Theorem
• Permutations & Combinations
• Mathematical Induction
• Statistics
• Probability — Basic
• Straight Lines
• Circles
• Parabola
• Ellipse
• Hyperbola
• Limits
• Continuity & Differentiability
• Applications of Derivatives
• Indefinite Integration
• Definite Integration
• Area Under Curves
• Differential Equations
• Vectors
• Three Dimensional Geometry
• Matrices
• Determinants
• Functions (Advanced)
• Probability — Advanced

Frequently asked questions

How many Differentiation questions are there for JEE Main?

PrepWiser has 38 Differentiation questions for JEE Main, grouped into 6 topics such as Derivatives of Standard Functions, Chain Rule and Implicit Differentiation.

Are these Differentiation questions from previous-year JEE Main papers?

Yes — most are genuine previous-year questions from past JEE Main papers, and the rest are practice questions written to match the JEE Main pattern and difficulty.

Where can I see the answers and solutions to these Differentiation questions?

Open any Differentiation question in PrepWiser (it is free) to attempt it; most come with a step-by-step solution.