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If  f(x) = logx(logx), then f'(x) at x = e is equal to

Option: 1

e


Option: 2

1/e


Option: 3

2/e


Option: 4

0


Answers (1)

best_answer

where t=logx

when x=e, t=1

\begin{aligned} & \frac{d y}{d t}=\frac{t x-(\log t)}{t^2}-1=\frac{1-\log t}{t^2} \\ \Rightarrow & \frac{d y}{d x}=\frac{d y}{d t} \cdot \frac{d t}{d x}=\frac{1-\log t}{t^2} \times \frac{1}{x} \\ \left.\frac{d y}{d x}\right|_{x=e}= & \frac{1-\log 1}{(1)^2} \cdot \frac{1}{e}=\frac{1}{e} \end{aligned}

Hence (B) is correct answer

Posted by

Ritika Harsh

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