If y = ( x)^ x , then dy dx = - Vidyadip

MCQ

If $y = {(\tan x)^{\cot x}}$, then ${{dy} \over {dx}} =$

✓
$y\cos {\rm{e}}{{\rm{c}}^2}x(1 - \log \tan x)$
B
$y\,{\rm{cos}}{\rm{e}}{{\rm{c}}^2}x(1 + \log \tan x)$
C
$y\cos {\rm{e}}{{\rm{c}}^2}x(\log \tan x)$
D
None of these

✓

Answer

Correct option: A.

$y\cos {\rm{e}}{{\rm{c}}^2}x(1 - \log \tan x)$

a
(a) $y = {(\tan x)^{\cot x}} \Rightarrow \log y = \cot x\log \tan x$

==> $\frac{1}{y}\frac{{dy}}{{dx}} = {\rm{cose}}{{\rm{c}}^{\rm{2}}}x - \log \tan x.{\rm{cose}}{{\rm{c}}^2}x$

==> $\frac{{dy}}{{dx}} = y{\rm{cose}}{{\rm{c}}^2}x(1 - \log \tan x)$.

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