WBJEE · Maths · Differentiation
Let \(f(x)>0\) for all \(x\) and \(f^{\prime}(x)\) exists for all \(x\). If \(f\) is the inverse function of \(h\) and \(h^{\prime}(x)=\frac{1}{1+\log x} \cdot\) Then, \(f^{\prime}(x)\) will be
- A \(1+\log (f(x))\)
- B \(1+f(x)\)
- C \(1-\log (f(x))\)
- D \(\log f(x)\)
Answer & Solution
Correct Answer
(A) \(1+\log (f(x))\)
Step-by-step Solution
Detailed explanation
Given, \[ h\{f(x)\}=x \] differentiating w.r.t. \(x\), we get \[ \begin{array}{r} h^{\prime}\{f(x)\}, f^{\prime}(x)=1 \\ f^{\prime}(x)=\frac{1}{h^{\prime}\{f(x)\}} \end{array} \]…
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