Question

Write the derivative of sinx with respect to cosx

Answer 1

$$\begin{gathered} \mathrm{Let}u=\sin x\mathrm{and}v=\cos x \\ \Rightarrow \frac{du}{dx}=\cos x\mathrm{and}\frac{dv}{dx}=-\sin x \\ \therefore \frac{{\displaystyle \frac{du}{dx}}}{{\displaystyle \frac{dv}{dx}}}=\frac{\cos x}{-\sin x} \\ \Rightarrow \frac{du}{dv}=-\cot x \end{gathered}$$