Question

Differentiate x² with respect to x³

Answer 1

\[\text{ Let u }= x^2 \text{ and }v = x^3 \]
\[ \Rightarrow \frac{du}{dx} = 2x \text { and } \frac{dv}{dx} = 3 x^2 \]
\[ \therefore \frac{du}{dv} = \frac{\frac{du}{dx}}{\frac{dv}{dx}} = \frac{2x}{3 x^2} = \frac{2}{3x}\]