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

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

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

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

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TopNewest\(\displaystyle f(g(x))=x\) , \(\displaystyle f'(g(x))g'(x)=1\implies \frac{g'(x)}{1+g^3(x)}=1 \implies g'(x)=1+g^3(x)\) – Aditya Narayan Sharma · 1 year, 4 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, 4 months ago

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