PYQ Vault
EbooksTutor

Derivative of an inverse function: g'(x) = 1/f'(g(x))

This type of question, asked 5 times: 4 May 2023 S1, 9 May 2023 S1, 9 May 2024 S2, 15 Apr 2026 S1, 19 Apr 2026 S2. All 5 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    4 May 2023 S1

    127
    If f(x)=x3+ex/2f(x)=x^3+e^{x/2} and g(x)=f−1(x)g(x)=f^{-1}(x), then the value of g′(1)g'(1) is

    Tap an option to check your answer.

  2. Question 2

    9 May 2023 S1

    147
    If f(x)=x2−xx2+2xf(x)=\frac{x^2-x}{x^2+2x} then ddxf−1(x)\frac{d}{dx}f^{-1}(x) at x=2x=2 is

    Tap an option to check your answer.

  3. Question 3

    9 May 2024 S2

    141
    If gg is the inverse of ff and f′(x)=11+x3f'(x) = \dfrac{1}{1+x^3}, then g′(x)g'(x) is

    Tap an option to check your answer.

  4. Question 4

    15 Apr 2026 S1

    73
    Let f(x)=3x3+4ex2f(x) = 3x^3 + 4e^{\frac{x}{2}} and g(x)=f−1(x)g(x) = f^{-1}(x). Then the value of g′(4)g'(4) is equal to...

    Tap an option to check your answer.

  5. Question 5

    19 Apr 2026 S2

    73
    If f(x)f(x) and g(x)g(x) are inverse functions of each other and f(x)=x+exf(x) = x + e^x, then g′(x)=g'(x) =...

    Tap an option to check your answer.