Let \(f(x)>0\) for all \(x\) and \(f^{\prime}(x)\) exists for all \(x\). If \(f\) is the inverse function of \(h\) and \(h^{\prime}(x)=\frac{1}{1+\log x} .\) Then \(f^{\prime}(x)\) will be

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Let \(f(x)>0\) for all \(x\) and \(f^{\prime}(x)\) exists for all \(x\). If \(f\) is the inverse function of \(h\) and \(h^{\prime}(x)=\frac{1}{1+\log x} .\) Then \(f^{\prime}(x)\) will be

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kritika · Answer 1 · 2021-12-27T04:29:55+0000

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Hint \(: h(f(x))=x \Rightarrow h^{\prime}(f(x)) \cdot f^{\prime}(x)=1 \Rightarrow f^{\prime}(x)=\frac{1}{h^{\prime}(f(x))} \Rightarrow f^{\prime}(x)=1+\log (f(x))\)

Let \(f(x)>0\) for all \(x\) and \(f^{\prime}(x)\) exists for all \(x\). If \(f\) is the inverse function of \(h\) and \(h^{\prime}(x)=\frac{1}{1+\log x} .\) Then \(f^{\prime}(x)\) will be

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