The derivative $\frac { d } { d x } \left[ \int _ { x } ^ { 3 } 2 ^ { t } d t \right]$ is

A) $2 ^ { x + 2 } - 8$
B) $8 - 2 ^ { x + 1 }$
C) $- 2 ^ { x + 1 }$
D) $8 - \frac { 2 ^ { x + 1 } } { x + 1 }$
E) $- 2 ^ { x }$

Question

The derivative $\frac { d } { d x } \left[ \int _ { x } ^ { 3 } 2 ^ { t } d t \right]$ is

A) $2 ^ { x + 2 } - 8$
B) $8 - 2 ^ { x + 1 }$
C) $- 2 ^ { x + 1 }$
D) $8 - \frac { 2 ^ { x + 1 } } { x + 1 }$
E) $- 2 ^ { x }$

Quizplus · Accepted Answer

The derivative of the integral from $x$ to a constant with respect to $x$ is the negative of the integrand evaluated at $x$, hence $-2^x$.

The Derivative ddx[∫x32tdt]\frac { d } { d x } \left[ \int _ { x } ^ { 3 } 2 ^ { t } d t \right]dxd​[∫x3​2tdt]