AP EAMCET · Maths · Differentiation
If \(f(x)=\log _{x^2}(\log x)\), then \(f^{\prime}(x)\) at \(x=e\) is
- A \(0\)
- B \(1\)
- C \(e^{-1}\)
- D \((2 e)^{-1}\)
Answer & Solution
Correct Answer
(D) \((2 e)^{-1}\)
Step-by-step Solution
Detailed explanation
\(f(x)=\log _{x^2}(\log x)\) \(\therefore f^{\prime}(x)=\frac{d}{d x} \log _{x^2}(\log x)\) \(=\frac{d}{d x}\left\{\frac{\log (\log x)}{\log \left(x^2\right)}\right\}\)…
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