Question

If f(x) = log_x (lnx) then f ′(x) at x = e is

• A. 1/e
• B. e
• C. e^1/e
• D. None of these

Answer 1

Answer: (A)

1/e

Answer 2

f(x) = log_x(log_ex) = $\frac{\log_{e}(\log_{e}x)}{\log_{e}x}$

f ′(x) = $\frac{(\log_{e}x)\left( \frac{1}{\log_{e}x}.\frac{1}{x} \right) - \frac{1}{x}.\log(\log x)}{(\log_{e}x)^{2}}$

⇒ f ′ (5) = $\frac{1 - \log 1}{e.(1)^{2}}$= 1/ e