How do you find the derivative of f(x) = (x^3-3)/x?

Jun 7, 2016

$2 x + \frac{3}{x} ^ 2$

Explanation:

Divide terms on numerator by x

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

now differentiate using the $\textcolor{b l u e}{\text{power rule}}$

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