Question

The derivative of x² with respect to x³ is __________________.

Answer 1

Let u(x) = x² and v(x) = x³.

$u\left(x\right)=x^2$

$\Rightarrow \frac{du}{dx}=2x$

$v\left(x\right)=x^3$

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

$\therefore \frac{du}{dv}=\frac{{\displaystyle \frac{du}{dx}}}{{\displaystyle \frac{dv}{dx}}}$

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

Thus, the derivative of x² with respect to x³ is $\frac{2}{3x}$.


The derivative of x² with respect to x³ is $\underline{\frac{2}{3x}}$.