# 3-8 Derivatives of Inverse Functions

## Learning Targets

## Concepts / Definitions

### Derivatives of Inverse Functions

If $f$ is differentiable at every point of an interval $I$ and $fâ(x)$ is never zero on $I$, then $f$ has an inverse, and $f^{-1}$ is differentiable at every point on the interval $f(I)$.

If $f^{-1}(a) = b$, the inverse function slope relationship relates the derivatives by the equation $(f^{-1})â(a) = \frac{1}{fâ(b)}$

### Proof of Inverse Sine

==>