### Home > CALC > Chapter 6 > Lesson 6.4.1 > Problem6-133

6-133.

Find $F^\prime(x)$.

1. $F ( x ) = \int _ { 5 } ^ { x ^ { 2 } } \operatorname { cos } ( \operatorname { ln } t ) d t$

The derivative of an integral is the original function, but this integral has bounds.

$F^\prime(x) = 2x\operatorname{cos}(\operatorname{ln}x^2)-0$

1. $F ( x ) = \int _ { \operatorname { sin } x } ^ { \operatorname { cos } x } \frac { 1 } { t ^ { 2 } + 1 } d t$

Notice the upper bound AND the lower bound.