# How do you differentiate  y = (x^(2/3) + 3) /( x^(1/5) + x)?

$y ' = \frac{\frac{7}{15} {x}^{- \frac{2}{15}} - \frac{1}{3} {x}^{\frac{2}{3}} - \frac{3}{5} {x}^{- \frac{4}{5}} - 3}{{x}^{\frac{1}{5}} + x} ^ 2$
Use $\frac{d}{\mathrm{dx}} \left(\frac{u}{v}\right)$=$\frac{v \cdot \frac{\mathrm{du}}{\mathrm{dx}} - u \cdot \frac{\mathrm{dv}}{\mathrm{dx}}}{v} ^ 2$
Let $u = {x}^{\frac{2}{3}} + 3$
and $v = {x}^{\frac{1}{5}} + x$