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

Apr 22, 2018

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

#### Explanation:

Rewrite the function with negative exponents, recalling that $\frac{1}{x} ^ a = {x}^{-} a$:

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

Apply the Power Rule, which tells us that if $f \left(x\right) = {x}^{n} , f ' \left(x\right) = n {x}^{n - 1} :$

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

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

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