# How do you find the derivative of 4x(x+x^(1/2))^(1/2)?

$f ' = 4 \cdot {\left(x + {x}^{\frac{1}{2}}\right)}^{\frac{1}{2}} + 2 x \cdot {\left(x + {x}^{\frac{1}{2}}\right)}^{- \frac{1}{2}}$
$f ' = 4 \cdot {\left(x + {x}^{\frac{1}{2}}\right)}^{\frac{1}{2}} + 4 x \cdot \left(\frac{1}{2}\right) {\left(x + {x}^{\frac{1}{2}}\right)}^{- \frac{1}{2}}$