# What is the derivative of 5/x^2?

May 30, 2016

$- \frac{10}{x} ^ 3$

#### Explanation:

Begin by expressing $\frac{5}{x} ^ 2 = 5 {x}^{-} 2$

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

$\frac{d}{\mathrm{dx}} \left(a {x}^{n}\right) = n a {x}^{n - 1}$

$\Rightarrow \frac{d}{\mathrm{dx}} \left(5 {x}^{-} 2\right) = \left(- 2\right) \times 5 {x}^{- 2 - 1} = - 10 {x}^{-} 3 = - \frac{10}{x} ^ 3$