If $F ( x ) = \int _ { 2 } ^ { 3 x } e ^ { t ^ { 4 } } d t \text {, find the value of } F ^ { \prime } ( 0 ) \text {. }$
A)1
B)2
C)3
D)4
E)6
F)8
G) $e ^ { 8 }$
H) $e ^ { 16 }$

Question

If $F ( x ) = \int _ { 2 } ^ { 3 x } e ^ { t ^ { 4 } } d t \text {, find the value of } F ^ { \prime } ( 0 ) \text {. }$ 
A)1
B)2
C)3
D)4
E)6
F)8
G) $e ^ { 8 }$ 
H) $e ^ { 16 }$

Quizplus · Accepted Answer

Using the Fundamental Theorem of Calculus and the chain rule, $ F'(x) = e^{(3x)^4} \cdot 3 $. Evaluating at $ x = 0 $, we get $ F'(0) = e^{0} \cdot 3 = 3 $.

If F(x)=∫23xet4dt, find the value of F′(0). F ( x ) = \int _ { 2 } ^ { 3 x } e ^ { t ^ { 4 } } d t \text {, find the value of } F ^ { \prime } ( 0 ) \text {. }F(x)=∫23x​et4dt, find the value of F′(0).

If $F ( x ) = \int _ { 2 } ^ { 3 x } e ^ { t ^ { 4 } } d t \text {, find the value of } F ^ { \prime } ( 0 ) \text {. }$