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Derivative of an Inverse Function
If $$y=f(x)$$ is invertible and:
$$f'(x)\neq0$$
then:
$$\frac{d}{dx}f^{-1}(x)=\frac{1}{f'(f^{-1}(x))}$$
Usage
- Used to differentiate inverse functions without explicitly finding their inverse equations.
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Derivative of an Inverse Function
If $$y=f(x)$$ is invertible and:
$$f'(x)\neq0$$
then:
$$\frac{d}{dx}f^{-1}(x)=\frac{1}{f'(f^{-1}(x))}$$
Usage
- Used to differentiate inverse functions without explicitly finding their inverse equations.
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