# How do you find the derivative of f(x)= (x^2-1)/x?

Feb 20, 2017

I would rewrite and avoid the quotient rule.

#### Explanation:

$f \left(x\right) = x - \frac{1}{x}$

So $f ' \left(x\right) = 1 + \frac{1}{x} ^ 2 = \frac{{x}^{2} + 1}{x} ^ 2$

If you like using the quotient rule

$f ' \left(x\right) = \frac{\left(2 x\right) \left(x\right) - \left({x}^{2} - 1\right) \left(1\right)}{x} ^ 2$

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

$= \frac{{x}^{2} + 1}{x} ^ 2$