JEE Mathematics

Derivatives of Functions: JEE Questions & Solutions

10 previous-year JEE Mathematics questions on Derivatives of Functions, each with a worked step-by-step solution.

Intermediate

Previous-year questions

  1. 01Let f(x) = x³ + x² f'(1) + 2x f''(2) + f'''(3), x ∈ ℝ. Then the value of f'(5) is:MCQMediumJEE 2026
  2. 02Let f: ℝ → ℝ be a twice differentiable function such that (sin x cos y)(f(2x + 2y) - f(2x - 2y)) = (cos x sin y)(f(2x + 2y) + f(2x - 2y))…MCQMediumJEE 2025
  3. 03Let f be a differentiable function on ℝ such that f(2) = 1 and f'(2) = 4. Let lim_(x → 0) ( f(2+x))^(3/x) = e^α. Then the number of times…MCQHardJEE 2025
  4. 04Given f(x) = x³ + x² f'(1) + x f''(2) + f'''(3), x ∈ ℝ. Then f'(10) is equal to:MCQMediumJEE 2024
  5. 05Let g(x) = 3f(x/3) + f(3 - x) where f''(x) > 0 for all x ∈ (0,3). If g is decreasing in (0, α) and increasing in (α,3), what is 8α?MCQMediumJEE 2024
  6. 06Suppose f(x) = (2^x + 2^(-x))tan x √tan⁻¹(x² - x + 1)/(7x² + 3x + 1)³. The value of f'(0) is equal to:MCQMediumJEE 2024
  7. 07Let f(x) = 2^x - x², x ∈ R. If m and n are respectively the number of points at which the curves y = f(x) and y = f'(x) intersect the…MCQEasyJEE 2024
  8. 08Let y = ln((1 - x²)/(1 + x²)), -1 < x < 1. Then at x = 1/2, the value of 225(y' - y'') is equal to:MCQMediumJEE 2024
  9. 09If f(x) = x³ - x² f'(1) + x f''(2) - f'''(3), x ∈ ℝ, then:MCQMediumJEE 2023
  10. 10If 2x^y + 3y^x = 20, then dy/dx at (2,2) is equal to:MCQMediumJEE 2023

Frequently asked questions

Our bank has 10 previous-year JEE Mathematics questions tagged to Derivatives of Functions, drawn from JEE papers between 2023 and 2026, including 1 from 2026 alone. Each comes with a full step-by-step solution.

Derivatives of Functions is rated Intermediate overall for JEE Mathematics. The PYQs on this page break down as 8 medium, 1 hard, 1 easy.

All 10 previous-year Derivatives of Functions questions in our bank are multiple-choice (MCQ) questions.

Based on recent paper analysis, Derivatives of Functions is worth about 1 mark in JEE Main. It sits in Limits, Continuity & Differentiability, a Class 12 Mathematics chapter.

More Limits, Continuity & Differentiability topics

Applications of Derivatives (Monotonicity, Extrema)45Limits39Continuity15Differentiability12

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