# How do you differentiate f(x) = x+x^(1/2) using the chain rule?

Dec 23, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = 1 + {x}^{- \frac{1}{2}} / 2$
$y = x + {x}^{\frac{1}{2}}$
$\frac{\mathrm{dy}}{\mathrm{dx}} = 1 + \frac{1}{2} {x}^{- \frac{1}{2}}$
$\frac{\mathrm{dy}}{\mathrm{dx}} = 1 + {x}^{- \frac{1}{2}} / 2$