Question

diffrenciate x/sinx with respect to x​

Answer 1

$\frac{d}{dx} \left(\frac{x}{ \sin x} \right) = \frac{d}{dx}(x \times \frac{1}{ \sin x}) \\ = x\frac{d}{dx} \left( \frac{1}{\sin x}\right) +\left(\frac{1}{\sin x}\right)\frac{d}{dx} x \\ = x \frac{d}{dx} ( \sin x)^{ - 1} + \frac{1} {\sin x}\\ = x \times - ( \sin x)^{ - 2} \frac{d}{dx} \sin x + \frac{1} {\sin x} \\ = - \frac{x}{ \sin^{2}x} \times \cos x + \frac{1} {\sin x} \\ = - \frac{ x}{ \sin x } \cot x + \frac{1} {\sin x} \\ = \frac{1 - x \cot x }{ \sin x }$