$\text { Find } F ^ { \prime } ( x ) \text { given } \bar { \digamma } ( x ) = \int _ { 1 } ^ { 6 x } \frac { 7 } { t } d t \text {. }$
A) $F F ^ {t } ( x ) = \frac { 13 } { x }$
B) $F ^ { t } ( x ) = \ln | 7 x |$
C) $F ^ { t } ( x ) = \frac { 6 } { x }$
D) $F ^ { t } ( x ) = \ln | 6 x |$
E) $F ^ { t } ( x ) = \frac { 7 } { x }$

Question

$\text { Find } F ^ { \prime } ( x ) \text { given } \bar { \digamma } ( x ) = \int _ { 1 } ^ { 6 x } \frac { 7 } { t } d t \text {. }$ 
A) $F F ^ {t } ( x ) = \frac { 13 } { x }$
B) $F ^ { t } ( x ) = \ln | 7 x |$
C) $F ^ { t } ( x ) = \frac { 6 } { x }$
D) $F ^ { t } ( x ) = \ln | 6 x |$
E) $F ^ { t } ( x ) = \frac { 7 } { x }$

Quizplus · Accepted Answer

The derivative of the integral $\bar{\digamma}(x) = \int_{1}^{6x} \frac{7}{t} dt$ with respect to $x$ is found using the Fundamental Theorem of Calculus and the chain rule: $F'(x) = \frac{7}{6x} \cdot 6 = \frac{7}{x}$.

Find F′(x) given ϝˉ(x)=∫16x7tdt. \text { Find } F ^ { \prime } ( x ) \text { given } \bar { \digamma } ( x ) = \int _ { 1 } ^ { 6 x } \frac { 7 } { t } d t \text {. } Find F′(x) given ϝˉ​(x)=∫16x​t7​dt.

$\text { Find } F ^ { \prime } ( x ) \text { given } \bar { \digamma } ( x ) = \int _ { 1 } ^ { 6 x } \frac { 7 } { t } d t \text {. }$