Let $g(x)$ be the inverse of an invertible function $f(x)$ which is differentia…

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Let $g(x)$ be the inverse of an invertible function $f(x)$ which is differentiable at $x=c$, then $g'(f(c))$ equals

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$ g(f(x))=x $ Differentiating, $ g'(f(x))\cdot f'(x)=1 $ $ \Rightarrow g'(f(x))=\frac{1}{f'(x)} $ $ \Rightarrow g'(f(c))=\frac{1}{f'(c)} $

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