Chapter 3: Derivatives - Practice Exercises - Page 177: 22

$y'=cos((x)^{1/2})+\frac{sin((x)^{1/2})}{x^{1/2}}$

Rewrite the equation: $y=2(x)^{1/2}sin((x)^{1/2})$ Take the derivative of the equation using Trigonometric derivative, Power Rule, and Chain Rule: $y'=2(x)^{1/2}\times cos((x)^{1/2})\times\frac{1}{2}x^{-1/2}+2\times\frac{1}{2}x^{-1/2}\times sin((x)^{1/2})$ $=cos((x)^{1/2})+\frac{sin((x)^{1/2})}{x^{1/2}}$