Answer
$\frac{dy}{dx} = \frac{4x^{0.2}}{5(x^{0.2}+x)^2} $
Work Step by Step
$y = \frac{x}{\sqrt[5] x + x}$
Take Derivative
$\frac{dy}{dx} = \frac{(1)(x^{0.2}+x)-(x)(0.2x^{-0.8}+1)}{(x^{0.2}+x)^2} = \frac{x^{0.2}+x-0.2x^{0.2}-x}{(x^{0.2}+x)^2} = \frac{x^{0.2}-0.2x^{0.2}}{(x^{0.2}+x)^2} = \frac{4x^{0.2}}{5(x^{0.2}+x)^2} $
