For an invertible differentiable function

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

For an invertible differentiable function ff, let aa be a real number such that f(a)=bf(a)=b. Which of the following expressions is equal to (f−1)′(b)(f^{-1})'(b)? (a) 1f′(a)\dfrac{1}{f'(a)} (b) f′(a)f'(a) (c) 1f′(b)\dfrac{1}{f'(b)} (d) −1f′(a)-\dfrac{1}{f'(a)}

Related theory

Browse the problem library