Question

What is the derivative of ${\cot }^{2}x$ ?

Answer 1

Determine the derivative of $co{t}^{2}x$.

Differentiate:

$$\begin{gathered} \frac{\mathrm{d}}{\mathrm{d}x}({\cot }^{2}x)=2\left(\cot \left(x\right)\right).\frac{\mathrm{d}}{\mathrm{d}x}(\cot (x\left)\right) \\ \Rightarrow =2\left(\cot \left(x\right)\right).(-{\mathrm{cosec}}^2(x\left)\right) \\ \Rightarrow =-2\left({\mathrm{cosec}}^2\left(x\right)\right).\left(\cot \left(x\right)\right) \end{gathered}$$

Hence, the derivative of $co{t}^{2}x$ is$\frac{\mathrm{d}}{\mathrm{d}x}({\cot }^{2}x)=-2{\mathrm{cosec}}^2\left(x\right)\cot \left(x\right)$.