Question

What is the derivative of an inverse function?

Answer 1

Derivative of an inverse function:

If $f^{-1}\left(x\right)$ is the inverse function of the function $f\left(x\right)$.

The derivative of an inverse function is,

$\frac{d}{dx}\left[f^{-1}\left(x\right)\right]=\frac{1}{f\text{'}\left(f^{-1}\left(x\right)\right)}$.