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

Jul 23, 2016

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

Explanation:

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

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\frac{d}{\mathrm{dx}} \left(a {x}^{n}\right) = n a {x}^{n - 1}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

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

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