First slide

Diffrentiation

Question

Differentiate the following functions with respect to x,
$\frac{x}{\sin x}$

Moderate

A

$\frac{\sin x - x \cos x}{\sin^{2} x}$
B

$\frac{\sin x - x \cos x}{\cos^{2} x}$
C

$\frac{\cos x - x \cos x}{\sin^{2} x}$
D

$\frac{\sin x - x \sin x}{\sin^{2} x}$

Solution

$\frac{d}{d x} (\frac{x}{\sin x}) = \frac{\sin x \frac{d}{d x} (x) - x \frac{d}{d x} (\sin x)}{(\sin x)^{2}} = \frac{(\sin x) (1) - x (\cos x)}{\sin^{2} x} = \frac{\sin x - x \cos x}{\sin^{2} x}$

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