The function is defined implicitly for near by the equation

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

Problem

The function hh is defined implicitly for xx near 11 by the equation xeh(x)+ln⁡(h(x))=3x e^{h(x)}+\ln(h(x)) = 3. Given that h(1)=1h(1)=1, compute (h−1)′(1)(h^{-1})'(1).

Related theory

Browse the problem library