Question

Differentiate the following functions with respect to x :

$\frac{x^3}{3}-2\sqrt{x}+\frac{5}{x^2}$

Answer 1

We have to differentiate f(x) with respect to x

$\frac{d}{dx}\left(\frac{x^3}{3}-2\sqrt{x}+\frac{5}{x^2}\right)$

$=\frac{1d^{(x{)}^3}}{3dx}-2\frac{d^{(\sqrt{x}})}{dx}+5\frac{d^{x^{-2}}}{dx}$

$=\frac{1}{3}.3x^2-2.\frac{1.1}{2\sqrt{x}}+5.(-2)x^{-3}$

$=x^2-x^{\frac{-1}{2}}-10x^{-3}$

$=x^2-\frac{1}{\sqrt{x}}-\frac{10}{x^3}$