Chapter 4 - Applications of the Derivative - 4.9 Antiderivatives - 4.9 Exercises - Page 329: 118

$$\frac{{\cos \sqrt x }}{{\sqrt x }}$$

$$\eqalign{ & = \frac{d}{{dx}}\left( {2\sin \sqrt x + C} \right) \cr & = \frac{d}{{dx}}\left( {2\sin \sqrt x } \right) + \frac{d}{{dx}}\left( C \right) \cr & {\text{by the chain rule}} \cr & = 2\left( {\cos \sqrt x } \right)\frac{d}{{dx}}\left( {\sqrt x } \right) + 0 \cr & = 2\left( {\cos \sqrt x } \right)\left( {\frac{1}{{2\sqrt x }}} \right) \cr & {\text{simplify}} \cr & = \left( {\cos \sqrt x } \right)\left( {\frac{1}{{\sqrt x }}} \right) \cr & = \frac{{\cos \sqrt x }}{{\sqrt x }} \cr} $$