Differentiate x x respect to x . - Vidyadip

Question

Differentiate $\frac{x}{\sin x}$ respect to $x .$

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Answer

$\text { Let } f ( x )=\frac{x}{\sin x}$
$\therefore f ( x )=\frac{d}{d x}\left(\frac{x}{\sin x}\right)$
$=\frac{\sin x \frac{d}{d x} x-x \frac{d}{d x} \sin x}{(\sin x)^2}$
$=\frac{\sin x \cdot 1-x \cdot \cos x}{\sin ^2 x}$
$=\operatorname{cosec} x-x \cot \times \operatorname{cosec} x$
$=(1-x \cot x) \cdot \operatorname{cosec} x$

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