Find the derivative.
-$y = \sqrt [ 8 ] { x ^ { 7 } } + x ^ { 7 e }$
A) $\frac { 7 } { 8 } x ^ { 1 / 8 } + 7 e x ^ { 7 e - 1 }$
B) $\frac { 7 } { 8 } x ^ { 1 / 8 } + 7 x ^ { 7 e - 1 }$
C) $\frac { 7 } { 8 } x ^ { - 1 / 8 } + 7 x ^ { 7 e - 1 }$
D) $\frac { 7 } { 8 } x ^ { - 1 / 8 } + 7 e x ^ { 7 e - 1 }$

Question

Quizplus · Accepted Answer

To take the derivative, we first use the chain rule for the first term and the power rule for the second term:
\begin{align*}
\frac{d}{dx}\left(\sqrt[8]{x^7}+x^{7e}ight)&=\frac{1}{8}\left(x^7ight)^{-7/8}\cdot7x^6+7ex^{7e-1}\
&=\frac{7}{8}x^{-1/8}+7ex^{7e-1}
\end{align*}
Therefore, the correct answer is $\boxed{	ext{(D)}}$.

Find the Derivative y=x78+x7ey = \sqrt [ 8 ] { x ^ { 7 } } + x ^ { 7 e }y=8x7​+x7e

Find the Derivative $y = \sqrt [ 8 ] { x ^ { 7 } } + x ^ { 7 e }$