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Mathematics - Differentiation

Practise 38 WBJEE previous year questions on Differentiation, compiled from papers spanning 2009 to 2025. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty WBJEE tests.

Differentiation has been asked in 16 of the 18 years of WBJEE papers analysed (2009–2026), with 38 questions in all. 24% of them were easy, 55% moderate and 21% tough. Most of its questions came from 2017, with 7 questions that year. In the last three years (2024–2026) it had 3 questions across 3 papers, about 1 per paper.

The chapter's 8 topics are not weighted equally: Higher order derivatives (11 questions, 29%), Differentiation of Inverse Trigonometric Functions (5 questions, 13%), and Differentiation of composite functions (5 questions, 13%) have been asked the most. Higher order derivatives has also led over the last five years, with 5 questions. Differentiation of Inverse Trigonometric Functions has produced the most tough questions (2).

  1. 1If ' ' is the inverse function of ' ' and , then the value of is2025Differentiation of Inverse Trigonometric Functions
  2. 2If a particle moves in a straight line according to the law , then the particle will come to rest at two points whose distance is [symbols h2024Parametric differentiation
  3. 3The acceleration of a particle after a time sec starting from rest is given by . Then the maximum velocity v and time T at attend this veloc2024Functional Equation
  4. 4Let \( ^{-1} ( {y}{b} )= _e ( {x}{n} )^n\), then \(A y_2+B y_1+C y=0\) is possible for2023Differentiation of composite functions
  5. 5The function \(y=e^{k x}\) satisfies \( ( {d^2 y}{d x^2}+ {d y}{d x} ) ( {d y}{d x}-y )=y {d y}{d x}\). It is valid for2023Higher order derivatives
  6. 6Given \( {d^2 y}{d x^2}+ x {d y}{d x}+4 y {cosec}^2 x=0\). Changing the independent variable \(x\) to \(z\) by the substitution \(z= {x}{2}\2023Higher order derivatives
  7. 7A missile is fired from the ground level rises \(x\) meters vertically upwards in \(t \), where \(x=100 t- {25}{2} t^2\). The maximum height2023Higher order derivatives
  8. 8If then2022Higher order derivatives
  9. 9If the transformation reduces the differential equation into the form then is equal to2022Higher order derivatives
  10. 10For , if then2021Differentiation of Inverse Trigonometric Functions
  11. 11The differential of at and for is2021Differentiation of composite functions
  12. 12Let . Then is2020Higher order derivatives
  13. 13Let for all and exists for all . If is the inverse function of and Then, will be2019Differentiation of composite functions
  14. 14Consider the function2019Differentiation of implicit functions
  15. 15Let for all Then for any fixed is2018Logarithmic differentiation
  16. 16The law of motion of a body moving along a straight line is vt. being its distance from a fixed point on the line at time and is its velocit2018Higher order derivatives
  17. 17Consider the non-constant differentiable function of one variable which obeys the relation If and then is2017Differentiation of composite functions
  18. 18If then is equal to2017Logarithmic differentiation
  19. 19Let and where is a real variable. Then, at is2017Differentiation of composite functions
  20. 20If then where is equal to2017Higher order derivatives
  21. 21Let Then, has2017Differentiation of implicit functions
  22. 22Let be twice continuously differentiable. Let Then,2017Higher order derivatives
  23. 23If being a non-negative integer, then the values of for which for all is2017Higher order derivatives
  24. 24If then the value of at is2016Logarithmic differentiation
  25. 25If then the value of is equal to2016Higher order derivatives
  26. 26The number of points at which the function cannot be differentiable, is2016Derivative of function and its inverse
  27. 27The points of the ellipse at which the ordinate decreases at the same rate at which the abscissa increases is/are given by2016Functional Equation
  28. 28A particle starts moving from rest from a fixed point in a fixed direction. The distance s from the fixed point at a timet is given by where2015Parametric differentiation
  29. 29For the curve the tangents are parallel to the -axis only at the points2013Derivative of function and its inverse
  30. 30Let Then, at equals2012Functional Equation
  31. 31For the value of is equal to2012Derivative of function and its inverse
  32. 32If \(x^2+y^2=4\), then \(y {d y}{d x}+x=\)2011Differentiation of implicit functions
  33. 33If \(y= {A}{x}+B x^2\), then \(x^2 {d^2 y}{d x^2}=\)2011Differentiation of implicit functions
  34. 34Let \( {f}( {x})= ^{-1} {x}\). Then \( {f}^{ }( {x})+ {f}^{ }( {x})\) is \(=0\), when \( {x}\) is equal to2011Differentiation of Inverse Trigonometric Functions
  35. 35If \(y= ^{-1} { {1+x^2}-1}{x}\), then \(y^{ }(1)=\)2011Differentiation of Inverse Trigonometric Functions
  36. 36If then the value of is2010Logarithmic differentiation
  37. 37The second order derivative of a with respect to a at is2009Parametric differentiation
  38. 38If , then the value of at is2009Differentiation of Inverse Trigonometric Functions

Frequently Asked Questions

1.How many questions are available for Differentiation?

This chapter includes 38 questions compiled from WBJEE papers spanning 2009 to 2025.

2.Are these questions only from WBJEE, or from other exams too?

These are WBJEE questions specifically for the Differentiation chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Differentiation an important chapter for WBJEE Mathematics?

Differentiation has appeared in 16 of the 18 years of WBJEE papers covered here, with 38 questions across 16 papers - about 2 per paper it appears in.

4.What is the difficulty level of Differentiation questions in WBJEE?

Of the 38 questions analysed for this chapter, 24% are easy, 55% moderate and 21% tough. 2017 had the most, with 7 questions.

5.Which topics in Differentiation should I focus on?

These topics have carried the most weightage in Differentiation:

  • Higher order derivatives - 11 questions (29%)
  • Differentiation of Inverse Trigonometric Functions - 5 questions (13%)
  • Differentiation of composite functions - 5 questions (13%)
  • Differentiation of Inverse Trigonometric Functions has produced the most tough questions (2).
6.Is Differentiation's weightage in WBJEE going up or down?

Across all 16 papers analysed, Differentiation has averaged about 2.4 questions per paper. In the last three years (2024–2026), that average has fallen, at about 1.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.