Differentiate the following functions:

(i) $x^{-3}$

$\frac{d}{d x} x^{n}=n x^{n-1}$

Differentiating w.r.t $x$,

$\frac{d}{d x} x^{-3}=-3 x^{-3-1}$

$=-3 x^{-4}$

(ii) $\sqrt[3]{\mathrm{x}}=\mathrm{x}^{\frac{1}{3}}$

Formula:-

$\frac{d}{d x} x^{n}=n x^{n-1}$

Differentiating w.r.t $\mathrm{x}$,

$\frac{d}{d x} X \frac{1}{3}=\frac{1}{3} X \frac{1}{3}-1$

$=\frac{1}{3} x^{-\frac{2}{3}}$