### Home > APCALC > Chapter 6 > Lesson 6.3.2 > Problem6-99

6-99.

Evaluate the following derivatives.

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

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

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

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

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