Question

Differentiate x² with respect to x³

Answer 1

$$\begin{gathered} \mathrm{Let}u=x^2\mathrm{and}v=x^3 \\ \Rightarrow \frac{du}{dx}=2x\mathrm{and}\frac{dv}{dx}=3x^2 \\ \therefore \frac{du}{dv}=\frac{{\displaystyle \frac{du}{dx}}}{{\displaystyle \frac{dv}{dx}}}=\frac{2x}{3x^2}=\frac{2}{3x} \end{gathered}$$