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Derivative of Inverse

Let \( g(x) = f^{-1}(x) \), and \(f'(x) = \dfrac1{1+x^3} \). Find \(g'(x) \).

Note: \(p'(x) \) denotes the derivative of \(p(x) \).

Note by D K
1 year, 6 months ago

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\(\displaystyle f(g(x))=x\) , \(\displaystyle f'(g(x))g'(x)=1\implies \frac{g'(x)}{1+g^3(x)}=1 \implies g'(x)=1+g^3(x)\)

Aditya Narayan Sharma - 1 year, 6 months ago

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Note that \[g'(f(x))=1+x^3\\\implies g'(x)=1+(g(x))^3\] To solve this de, use variable separition and partial fractions.

Deeparaj Bhat - 1 year, 6 months ago

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