For parts (a) and (b) below, explain why finding the derivative requires the use of the Chain Rule and the Product Rule. Then find the derivative.

1. $\frac { d } { d x } \sqrt { \operatorname { sin } x \operatorname { cos } x }$

   Hint (a):

   This derivative requires BOTH the Chain Rule and the Product Rule.

2. $\frac { d } { d x } ( \sqrt { x } \operatorname { sin } ( x ^ { 3 } ) )$

   Hint (b):

   This derivative also requires the Chain Rule and the Product Rule, but in the opposite order as part (a).