Answer
$y'=(2x+x^{1/2})(x+x^{1/2})^{-1/2}+4(x+x^{1/2})^{1/2}$
Work Step by Step
Rewrite the equation: $y=4x(x+x^{1/2})^{1/2}$
Take the derivative of the equation using Product Rule, Power Rule, and Chain Rule:
$y'=4x\times\frac{1}{2}(x+x^{1/2})^{-1/2}\times(1+\frac{1}{2}x^{-1/2})+4(x+x^{1/2})^{1/2}$
$=(2x+x^{1/2})(x+x^{1/2})^{-1/2}+4(x+x^{1/2})^{1/2}$
