Evaluate the following derivatives.

1. ​$\frac { d } { d x } \int _ { 0 } ^ { \operatorname { sin } ( x ) } 3 ^ { t ^ { 2 } } d t$

   Hint (a):

   $\ne3^{\sin2(x)}$
   Explain why not.

   Answer (a):

   $= \cos(x)\cdot3^{\sin^2(x)}$
   Notice that the Chain Rule was applied to BOTH bounds.

2. $\frac { d } { d x } \int _ { \operatorname { sin } ( x ) } ^ { 0 } \operatorname { ln } ( t ^ { 2 } + 1 ) d t$

   Hint (b):

   Careful! Is the answer going to be positive or negative?