The differential coefficient of f[ (x)] when f(x) = x is - Vidyadip

MCQ

The differential coefficient of $f[\log (x)]$ when $f(x) = \log x$ is

A
$x\log x$
B
${x \over {\log x}}$
✓
${1 \over {x\log x}}$
D
${{\log x} \over x}$

✓

Answer

Correct option: C.

${1 \over {x\log x}}$

c
(c) $\because f(x)=\log x$ ;

$\therefore f[\log x] = \log \log x$

$f'[\log x] = \frac{1}{{\log x}}.\frac{d}{{dx}}\log x = \frac{1}{{x\log x}}$.

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