Answer
$y'=\frac{cos\sqrt x}{2\sqrt x}-\frac{sin\sqrt x}{2}$
Work Step by Step
Start with the function: $y=\sqrt x cos\sqrt x$.
Let $u=\sqrt x=x^{1/2}$. Then
$y=u cos (u)$.
Use the product rule to differentiate: $y'=u'cos(u)-uu'sin(u)$.
Use power rule to find u': $u'=\frac{1}{2}x^{-1/2}$.
Substitute expressions for u and u' into y' to find the answer:
$y'=\frac{cos\sqrt x}{2\sqrt x}-\frac{sin\sqrt x}{2}$.
