## Calculus: Early Transcendentals 8th Edition

$y'=\frac{cos\sqrt x}{2\sqrt x}-\frac{sin\sqrt x}{2}$
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: $y'=\frac{cos\sqrt x}{2\sqrt x}-\frac{sin\sqrt x}{2}$.