Continuity and Differentiability — Class 12 Maths Solution

Derivative of ${x^2}$ w.r.t. ${x^3}$ is $\frac{2}{{3x}}$

Let $u = {x^2}$ and $v = {x^3}$
therefore,$\quad \frac{{du}}{{dx}} = 2x$ and $\frac{{dv}}{{dx}} = 3{x^2}$

$\Rightarrow$ $\quad \frac{{du}}{{dv}} = \frac{{2x}}{{3{x^2}}} = \frac{2}{{3x}}$