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Mathematics
The derivative of ( cot x) sin x+( tan x) cos x with respect to x is
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Q. The derivative of $(\cot x)^{\sin x}+(\tan x)^{\cos x}$ with respect to $x$ is
A
$(\cot x)^{\sin x}[\sec x+\cos x \log (\cot x)]+(\tan x)^{\cos x}[\operatorname{cosec} x-\sin x \log (\tan x)]$
B
$(\cot x)^{\sin x}[-\sec x+\cos x \log (\cot x)]+(\tan x)^{\cos x}[\cos e c x+\sin x \log (\tan x)]$
C
$(\cot x)^{\sin x}[\sec x-\cos x \log (\cot x)]+(\tan x)^{\cos x}[\operatorname{cosec} x-\sin x \log (\tan x)]$
D
$(\cot x)^{\sin x}[-\sec x+\cos x \log (\cot x)]+(\tan x)^{\cos x}[\cos e c x-\sin x \log (\tan x)]$
Solution:
$\frac{d}{d x}\left[f(x)^{g(x)}\right]=f(x)^{g(x)}\left[g(x) \frac{f^{'}(x)}{f(x)}+g^{'}(x) \log (f(x))\right]$