d dx ( x) = - Vidyadip

MCQ

${d \over {dx}}(\log \tan x) = $

A
$2\sec 2x$
✓
$2\,{\rm{cosec }}2x$
C
$\sec 2x$
D
${\rm{cosec}}\,2x$

✓

Answer

Correct option: B.

$2\,{\rm{cosec }}2x$

b
(b) $\frac{d}{{dx}}(\log \tan x) = \frac{1}{{\tan x}}{\sec ^2}x = \frac{{\cos x}}{{{{\cos }^2}x\sin x}}$

$ = \frac{2}{2}\frac{1}{{\cos x\sin x}} = 2\,{\rm{cosec}}\,2x$.

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