JAMB 1995 · UME · Q38

The derivative of $\text{cosec}\,x$ is

Worked solution (try it first)

Write $\text{cosec}\,x = (\sin x)^{-1}$ and use the chain rule: the derivative is $-(\sin x)^{-2}\cos x = -\dfrac{\cos x}{\sin^2 x}$ .
Split it as $-\dfrac{\cos x}{\sin x} \times \dfrac{1}{\sin x} = -\cot x\,\text{cosec}\,x$ , option B.