If y = x + x x - x , then dy dx = - Vidyadip

MCQ

If $y = {{\tan x + \cot x} \over {\tan x - \cot x}},$ then ${{dy} \over {dx}} = $

A
$2\tan 2x\sec 2x$
B
$\tan 2x\sec 2x$
C
$ - \tan 2x\sec 2x$
✓
$ - 2\tan 2x\sec 2x$

✓

Answer

Correct option: D.

$ - 2\tan 2x\sec 2x$

d
(d) $y = \frac{{\tan x + \cot x}}{{\tan x - \cot x}} = - \frac{{1 + {{\tan }^2}x}}{{1 - {{\tan }^2}x}} = - \sec 2x$

$ \Rightarrow \frac{{dy}}{{dx}} = - 2\sec 2x\tan 2x$.

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