If y = _ x ( x), then ( dy dx )_ /4 = - Vidyadip

MCQ

If $y = {\log _{\sin x}}(\tan x),$ then ${\left( {{{dy} \over {dx}}} \right)_{\pi /4}} = $

A
${4 \over {\log 2}}$
B
$ - 4\log 2$
✓
${{ - 4} \over {\log 2}}$
D
None of these

✓

Answer

Correct option: C.

${{ - 4} \over {\log 2}}$

c
(c) $y = \frac{{\log \tan x}}{{\log \sin x}}$

==> $\frac{{dy}}{{dx}} = \frac{{(\log \sin x)\left( {\frac{{{{\sec }^2}x}}{{\tan x}}} \right) - (\log \tan x)(\cot x)}}{{{{(\log \sin x)}^2}}}$

==> ${\left( {\frac{{dy}}{{dx}}} \right)_{\pi /4}} = \frac{{ - 4}}{{\log 2}}$ (On simplification).

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