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Derivative of the Inverse Function
If $$y=f(x)$$ and $$f$$ is invertible, then:
$$\frac{dy}{dx}=\frac{1}{dx/dy}$$
Therefore:
$$\frac{d}{dx}[f^{-1}(x)]=\frac{1}{f'(f^{-1}(x))}$$
Usage
- Used to differentiate inverse functions without explicitly finding the inverse.
