Question

find the derivative by qutient rule of cot x

Answer 1

$$\begin{gathered} \mathrm{Let}y=cotx \\ \Rightarrow y=\frac{\cos x}{\sin x} \\ \Rightarrow \frac{dy}{dx}=\frac{\sin x\times \left(-\sin x\right)-\cos x\times \cos x}{{\sin }^{2}x} \\ \Rightarrow \frac{dy}{dx}=\frac{-\left({\cos }^{2}x+{\sin }^{2}x\right)}{{\sin }^{2}x}=\frac{-1}{{\sin }^{2}x}=-{\mathrm{cosec}}^{2}x \end{gathered}$$