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JEE Main Differentiation and Application of Derivatives questions with solutions

Continuity, differentiability, differentiation techniques, tangents, maxima and minima and monotonicity. 19 questions from our 2016–2025 JEE Main pattern papers, from the Class 12 Mathematics syllabus. Each has the answer and a full solution.

Also practise: Differentiation and Application of Derivatives for JEE Advanced

JEE Main 2025

If x=2(t-sin t) and y=2(1-cos t), then (d^2y)/(dx^2 at t=(π)/(2) equalsJEE Main 2025 · medium
The least value of the square of the distance of a point of the parabola y=x^2 from the point (0,3) isJEE Main 2025 · medium

JEE Main 2024

Let y=x^x with x>0. The value of dy/dx at x=1 isJEE Main 2024 · medium
Over the closed interval [0,3], the greatest value attained by f(x)=2x^3-9x^2+12x+1 isJEE Main 2024 · medium

JEE Main 2022

If y=tan ^-1 ((1+x)/(1-x)), then dy/dx at x=2 isJEE Main 2022 · medium
The minimum value of f(x)=x^3-12x+5 on the interval [0,3] isJEE Main 2022 · medium

JEE Main 2021

The number of points in mathbb R at which f(x)=|x^2-3x+2|+|x-3| is not differentiable isJEE Main 2021 · easy
Let f(x)=sin ^-1 ((2x)/(1+x^2). Then f'(2) equalsJEE Main 2021 · medium
A rectangle has two vertices on the x-axis and the other two on the semicircle y=√(25-x^2. The maximum possible area of the rectangle isJEE Main 2021 · medium

JEE Main 2020

Let f(x)=(sin 3x+asin x)/(x^3 for x≠0. If f can be made continuous at x=0 by defining f(0)=b, then a+b equalsJEE Main 2020 · medium
Let f(x)=x^3+2x-3 and let g be the inverse function of f. Then g''(0) equalsJEE Main 2020 · medium

JEE Main 2019

Let [t] denote the greatest integer not exceeding t. The number of points in the open interval (0,3) at which g(x)=[x^2] is discontinuous isJEE Main 2019 · medium
If x=t^2 and y=t^3-3t for t>0, then (d^2y)/(dx^2 at t=2 equalsJEE Main 2019 · medium

JEE Main 2018

Let f(x)=x^3 for x≤1 and f(x)=ax^2+bx+c for x>1. If f, f' and f'' are all continuous at x=1, then abc equalsJEE Main 2018 · medium

JEE Main 2017

Let f(x)=(sin 2x+asin x)/(x^3 for x≠0 and f(0)=b. If f is continuous at x=0, then a+b equalsJEE Main 2017 · medium
For the function y=x^x defined on x>0, the value of its derivative at the point x=1 isJEE Main 2017 · medium
The local maximum value of f(x)=x^3-12x+5 isJEE Main 2017 · medium
The equation of the tangent to the curve y=x^2+3x at the point where x=1 isJEE Main 2017 · easy

JEE Main 2016

If y=sin ^-1 (2x√(1-x^2) for |x|<(1)/(√2), then dy/dx at x=1/2 equalsJEE Main 2016 · hard

Other Mathematics topics

Area Under Curves 7 Binomial Theorem 12 Complex Numbers 10 Conic Sections 5 Differential Equations 9 Indefinite and Definite Integrals 16 Limits 9 Matrices and Determinants 19 Permutations and Combinations 10 Probability 9 Quadratic Equations 9 Sequences and Series 9 Sets, Relations and Functions 10 Statistics 6 Straight Lines and Circles 9 Three Dimensional Geometry 14 Trigonometry and Inverse Trigonometric Functions 9 Vector Algebra 8