WBJEE · Maths · Differentiation
If ' \(f\) ' is the inverse function of ' \(g\) ' and \(g^{\prime}(x)=\frac{1}{1+x^n}\), then the value of \(f^{\prime}(x)\) is
- A \(1+\{f(x)\}^n\)
- B \(1-\{f(x)\}^n\)
- C \(\{1+f(x)\}^n\)
- D \(\{f(x)\}^n\)
Answer & Solution
Correct Answer
(A) \(1+\{f(x)\}^n\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & g^{-1}(x)=f(x) \\ & g^{\prime}(x)=\frac{1}{1+x^n} \quad \Rightarrow g^{\prime}\left(g^{-1}(x)\right)=\frac{1}{1+\left(g^{-1}(x)\right)^n}=\frac{1}{1+(f(x))^n} \\ & g\left(g^{-1}(x)\right)=x \\ & g^{\prime}\left(g^{-1}(x)…
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