Differentiate the following functions with respect to x: ( 4 + 2 … - Vidyadip

Question

Differentiate the following functions with respect to x:
$\log\Big\{\cot\Big(\frac{\pi}{4}+\frac{\pi}{2}\Big)\Big\}$

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Answer

$\frac{\text{d}}{\text{dx}}\Big[\log\Big\{\cot\Big(\frac{\Pi}{4}+\frac{\pi}{2}\Big)\Big\}\Big]$
$\frac{1}{\cot\Big(\frac{\pi}{4}+\frac{\text{x}}{2}\Big)}\times\Big(-\text{cosec}^2\Big(\frac{\pi}{4}+\frac{\text{x}}{2}\Big)\Big)\times\frac{1}{2}$
$\frac{-1}{2\cos\Big(\frac{\pi}{4}+\frac{\text{x}}{2}\Big)\sin\Big(\frac{\pi}{4}+\frac{\text{x}}{2}\Big)}=-\frac{1}{\sin2\Big(\frac{\pi}{4}+\frac{\text{x}}{2}\Big)}$
$=-\frac{1}{\sin2\Big(\frac{\pi}{4}+\frac{\text{x}}{2}\Big)}=-\frac{1}{\cos\text{x}}=-\sec\text{x}$

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