Differentiation Question 280

Question: If $ y=\log \log x $ , then $ e^{y}\frac{dy}{dx}= $

[MP PET 1994, 95]

Options:

A) $ \frac{1}{x\log x} $

B) $ \frac{1}{x} $

C) $ \frac{1}{\log x} $

D) $ e^{y} $

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Answer:

Correct Answer: B

Solution:

$ y={\log _{e}}{\log _{e}}x\Rightarrow e^{y}={\log _{e}}x\Rightarrow e^{y}\frac{dy}{dx}=\frac{1}{x} $ .