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Mathematics - Differentiation

Practise 69 KCET previous year questions on Differentiation, compiled from papers spanning 2007 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty KCET tests.

Differentiation has been asked in 20 of the 20 years of KCET papers analysed (2007–2026), with 69 questions in all. 22% of them were easy, 54% moderate and 25% tough. Most of its questions came from 2022, with 6 questions that year. In the last three years (2024–2026) it had 6 questions across 3 papers, about 2 per paper.

The chapter's 9 topics are not weighted equally: Differentiation of composite functions (20 questions, 29%), Differentiation of Inverse Trigonometric Functions (8 questions, 12%), and Parametric differentiation (8 questions, 12%) have been asked the most. Over the last five years the most frequent topics have been Derivative of f(x) wrt g(x) (3), Differentiation of Inverse Trigonometric Functions (2), and Higher order derivatives (2). Higher order derivatives has produced the most tough questions (3).

  1. 1If , then2026Differentiation of implicit functions
  2. 2If , then2026Differentiation of Inverse Trigonometric Functions
  3. 3If , then (a) (b) (c) (d)2025Differentiation of composite functions
  4. 4If , then at is2025Parametric differentiation
  5. 5The derivative of with respect to is2025Derivative of f(x) wrt g(x)
  6. 6If , then at is2024Logarithmic differentiation
  7. 7If , then is equal to2023Functional Equation
  8. 8If and then is2023Derivative of f(x) wrt g(x)
  9. 9If , then is2022Differentiation of Inverse Trigonometric Functions
  10. 10If where is a parameter, then at is equal to2022Derivative of f(x) wrt g(x)
  11. 11If , then at is2022Higher order derivatives
  12. 12If , then the derivative of at is2022Functional Equation
  13. 13If , then at is2022Derivative of function and its inverse
  14. 14If the ordered pair at is equal to2022Higher order derivatives
  15. 15If and are fixed non-zero constants, then the derivative of is , where2021Differentiation of composite functions
  16. 16If , then is equal to2021Differentiation of composite functions
  17. 17For constant is2021Logarithmic differentiation
  18. 18Consider the following statements Statement 1 : If , then Statement 2 : If and2021Logarithmic differentiation
  19. 19If , then at is equal to2021Higher order derivatives
  20. 20If , then is2020Parametric differentiation
  21. 21The right hand and left hand limit of the function are respectively.2020Logarithmic differentiation
  22. 22If is a square matrix of order 3 and , then adj. is2020Differentiation of composite functions
  23. 23If is continuous at , then the value of is2020Differentiation of Inverse Trigonometric Functions
  24. 24If \( [3]{y} {x}= [6]{(x+y)^{5}} \), then \( {d y}{d x}= \)2019Differentiation of composite functions
  25. 25If \( [x] \) represents the greatest integer function and \( f(x)=x-[x]- x \) then \( f^{ } ( {I}{2} )= \)2019Differentiation of composite functions
  26. 26If \( f(x)= ^{-1} [ {2^{x+1}}{1+4^{x}} ] \), then \( f^{ }(0)= \)2019Differentiation of Inverse Trigonometric Functions
  27. 27If \( x= {asec}^{2} , y= {atan}^{2} \) then \( {d^{2} y}{d x^{2}}= \)2019Higher order derivatives
  28. 28Let \( f(x)=x- {1}{x} \) then \( f^{ }(-1) \) is2018Differentiation of composite functions
  29. 29If \( y=x (a+y) \) with \( a 1 \), then \( {d y}{d x} \) is equal to2018Differentiation of implicit functions
  30. 30If \( f(x)=| x- x| \), then \( f^{ } ( { }{6} ) \) is equal to2018Differentiation of implicit functions
  31. 31If \( y= {x+ {x+ {x+ }}} \), then \( {d y}{d x}= \)2018Differentiation of implicit functions
  32. 32If \( y= ( x) \) then \( {d^{2} y}{d x^{2}} \) is equal to2017Parametric differentiation
  33. 33\( {x^{2}+2 x+5} d x \) is equal to2017Higher order derivatives
  34. 34The area of the region bounded by the curve \( y=x^{2} \) and the line \( y=16 \) is2017Differentiation of composite functions
  35. 35General solution of differential equation \( {d y}{d x}+y=1(y 1) \) is2017Differentiation of Inverse Trigonometric Functions
  36. 36If \( y=e^{ ^{-1} (t^{2}-1 )} \& x=e^{ ^{-1} ( {1}{t^{2}-1} )} \) then \( {d y}{d x} \) is equal to2016Parametric differentiation
  37. 37If \( x^{y}=e^{x-y} \) then \( {d y}{d x} \) is equal to2016Differentiation of implicit functions
  38. 38If \( x^{m} y^{n}=(x+y)^{m+n} \) then \( {d y}{d x} \) is equal to2016Differentiation of implicit functions
  39. 39The differential coefficient of \( _{10} x \) with respect to \( _{x} 10 \) is2016Derivative of f(x) wrt g(x)
  40. 40The slope of the tangent to the curve \( x=t^{2}+3 t-8, y=2 t^{2}-2 t-5 \) at the point \( (2,-1) \) is2016Parametric differentiation
  41. 41If \( ^{-1} (x^{2}+y^{2} )= \) then \( {d y}{d x} \) is equal to2016Differentiation of implicit functions
  42. 42Area bounded by \( y=x^{3}, y=8 \) and \( x=0 \) is2015Functional Equation
  43. 43Let \(a=i+j+k, b=i-j+k\) and \(c=i-j-k\) be three vectors. A vector \(v\) in the plane of a and \(b\), whose projection on \(c\) is \(1 / {32015Parametric differentiation
  44. 44\( e^{x} ( {1+ x}{1+ x} ) d x \) is2015Functional Equation
  45. 45If \( {(x+1)^{2}}{x^{3}+x}= {A}{x}+ {B x+C}{x^{2}+1} \), then \( {cosec}^{-1} ( {1}{A} )+ ^{-1} ( {1}{B} )+ ^{-1} C= \)2015Parametric differentiation
  46. 46If \( {P}= | {array}{ll}x & 1 \\ 1 & x {array} | \) and \( {Q}= | {array}{lll}x & 1 & 1 \\ 1 & x & 1 \\ 1 & 1 & x {array} | \),then \( {d Q}2015Differentiation of composite functions
  47. 47For any two real numbers, an operation \( * \) defined by \( a * b=1+a b \) is2014Logarithmic differentiation
  48. 48The value of \( (2 ^{-1} 0.8 ) \) is equal to2014Functional Equation
  49. 49If and , then is equal to2013Differentiation of Inverse Trigonometric Functions
  50. 50If . Then, is equal to2013Differentiation of composite functions

Frequently Asked Questions

1.How many questions are available for Differentiation?

This chapter includes 69 questions compiled from KCET papers spanning 2007 to 2026.

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

These are KCET 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 KCET Mathematics?

Differentiation has appeared in 20 of the 20 years of KCET papers covered here, with 69 questions across 20 papers - about 3 per paper it appears in.

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

Of the 69 questions analysed for this chapter, 22% are easy, 54% moderate and 25% tough. 2022 had the most, with 6 questions.

5.Which topics in Differentiation should I focus on?

These topics have carried the most weightage in Differentiation:

  • Differentiation of composite functions - 20 questions (29%)
  • Differentiation of Inverse Trigonometric Functions - 8 questions (12%)
  • Parametric differentiation - 8 questions (12%)
  • Higher order derivatives has produced the most tough questions (3).
6.Is Differentiation's weightage in KCET going up or down?

Across all 20 papers analysed, Differentiation has averaged about 3.5 questions per paper. In the last three years (2024–2026), that average has fallen, at about 2.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.