d dx |x| = ......,(x 0) - Vidyadip

MCQ

${d \over {dx}}\log |x|{\rm{ }} = ......,(x \ne 0)$

✓
${1 \over x}$
B
$ - {1 \over x}$
C
$x$
D
$ - x$

✓

Answer

Correct option: A.

${1 \over x}$

a
(a) $\log |x|\, = \log x$, if $x > 0$$ = \log ( - x)$, if $x < 0$

Hence $\frac{d}{{dx}}\left\{ {\log |x|} \right\} = \frac{1}{x}$, if $x > 0$

$ = \left( {\frac{1}{{ - x}}} \right)( - 1) = \frac{1}{x}$, if $x < 0$

Thus $\frac{d}{{dx}}\left\{ {\log |x|} \right\} = \frac{1}{x}$, if $x \ne 0$.

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