Find $y ^ { \prime }$ . $y = \ln ( 5 x + 7 ) ^ { 1 / 8 }$
A) $\frac { 5 } { 8 ( 5 x + 7 ) }$
B) $\frac { 7 } { 5 ( 5 x + 7 ) }$
C) $\frac { 7 } { 8 ( 5 x + 7 ) }$
D) $\frac { 35 } { 8 ( 5 x + 7 ) }$
E) $\frac { 40 } { 7 ( 5 x + 7 ) }$

Question

Quizplus · Accepted Answer

To find $y'$, apply the chain rule to the function $y = \ln(5x + 7)^{1/8}$. First, differentiate the outer function, $\ln(u)$, with respect to $u$, which gives $1/u$. Then, differentiate the inner function, $u = (5x + 7)^{1/8}$, with respect to $x$, which gives $\frac{1}{8}(5x + 7)^{-7/8} \cdot 5$. Combining these gives $\frac{5}{8(5x + 7)}$.

Find y′y ^ { \prime }y′ y=ln⁡(5x+7)1/8y = \ln ( 5 x + 7 ) ^ { 1 / 8 }y=ln(5x+7)1/8

Find $y ^ { \prime }$ $y = \ln ( 5 x + 7 ) ^ { 1 / 8 }$