Question

derivative of cos^2 x

Answer 1

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