# How do you find the derivative of root5(x^-5)?

$\frac{d \left(\sqrt[5]{{x}^{- 5}}\right)}{\mathrm{dx}} = - \frac{1}{x} ^ 2$
$\sqrt[5]{{x}^{- 5}} = {\left({x}^{- 5}\right)}^{\frac{1}{5}} = {x}^{\left(- 5\right) \times \left(\frac{1}{5}\right)} = {x}^{-} 1$
As $\frac{d \left({x}^{-} 1\right)}{\mathrm{dx}} = - 1 \cdot {x}^{- 2} = - \frac{1}{x} ^ 2$
Hence $\frac{d \left(\sqrt[5]{{x}^{- 5}}\right)}{\mathrm{dx}} = - \frac{1}{x} ^ 2$