### Home > CALC > Chapter 6 > Lesson 6.3.3 > Problem6-106

6-106.

Evaluate the following derivatives.

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

≠ 3sin2(x)
Explain why not.

= cos(x)3sin2(x)
Notice that the Chain Rule was applied to BOTH bounds.

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

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