# How do you find the derivative of (x^2-2)/(x)?

May 24, 2015

At first sight we might think of using the quotient rule, but I'd rather operate a division here and simplify things for us. That'll be not only faster but show knowledge on derivation.

We see this function $\frac{{x}^{2} - 2}{x}$ can be rewritten as

${x}^{2} / x - \frac{2}{x}$

In turn, it can be rewritten as

$x - 2 {x}^{-} 1$

Now, derivating this sounds easier, doesn't it?

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