Question

Find the derivative of the following:
$\frac{2}{x+1}-\frac{x^2}{3x-1}$.

Answer 1

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

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

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

$=\left(\frac{-2}{{(x+1)}^2}\right)-\frac{6x^2-2x-3x^2}{{(3x-1)}^2}$

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