Question

Differentiate the following functions with respect to x :

$\frac{(x^3+1)(x-2)}{x^2}$

Answer 1

We have,

$\frac{d}{dx}\frac{\left\{\right(x^3+1\left)\right(x-2\left)\right\}}{x^2}$

$=\frac{d}{dx}\frac{\{x^4-2x^3+x-2\}}{x^2}$

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

$=\frac{d}{dx}\left(x^2\right)-2\frac{dx}{dx}+\frac{d{x}^{-1}}{dx}-2\frac{d{x}^{-2}}{dx}$

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

$=2x-2-\frac{1}{x^2}+\frac{4}{x^3}$