Question
Differentiate the following functions with respect to x:
$\log\Big\{\cot\Big(\frac{\pi}{4}+\frac{\pi}{2}\Big)\Big\}$
$\log\Big\{\cot\Big(\frac{\pi}{4}+\frac{\pi}{2}\Big)\Big\}$
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$\tan ^{-1}\left(\frac{a+b \tan x}{b-a \tan x}\right)$
$e^{x+y}=\cos (x-y)$
$\tan ^{-1}\left(\frac{2^{x+2}}{1-3\left(4^x\right)}\right)$
$x^{\tan ^{-1} x}$