d dx [ ( x + 1 x ) ] = - Vidyadip

MCQ

${d \over {dx}}\left[ {\log \left( {x + {1 \over x}} \right)} \right] = $

A
$\left( {x + {1 \over x}} \right)$
B
${{\left( {1 + {1 \over {{x^2}}}} \right)} \over {\left( {1 + {1 \over x}} \right)}}$
✓
${{\left( {1 - {1 \over {{x^2}}}} \right)} \over {\left( {x + {1 \over x}} \right)}}$
D
$\left( {1 + {1 \over x}} \right)$

✓

Answer

Correct option: C.

${{\left( {1 - {1 \over {{x^2}}}} \right)} \over {\left( {x + {1 \over x}} \right)}}$

c
(c) $\frac{d}{{dx}}\left\{ {\log \left( {x + \frac{1}{x}} \right)} \right\} = \frac{1}{{x + \frac{1}{x}}} \times \frac{d}{{dx}}\left( {x + \frac{1}{x}} \right) $

$= \frac{1}{{\left( {x + \frac{1}{x}} \right)}}\left( {1 - \frac{1}{{{x^2}}}} \right)$

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