Chapter 4 - Applications of the Derivative - 4.9 Antiderivatives - 4.9 Exercises - Page 329: 120

$$\boxed{{x^2}\cos {x^3}}$$

$$\eqalign{ & \text{differentiate} \cr & = \frac{d}{{dx}}\left( {\frac{1}{3}\sin {x^3} + C} \right) \cr & = \frac{1}{3}\frac{d}{{dx}}\left( {\sin {x^3}} \right) + \frac{d}{{dx}}\left( C \right) \cr & {\text{by the chain rule}} \cr & = \frac{1}{3}\left( {\cos {x^3}} \right)\frac{d}{{dx}}\left( {{x^3}} \right) \cr & = \frac{1}{3}\left( {\cos {x^3}} \right)\left( {3{x^2}} \right) \cr & {\text{simplify}} \cr & = {x^2}\cos {x^3} \cr} $$