Differentiate the given function. $y = \sqrt { 6 x ^ { 6 } + 8 x }$
A) $\frac { 1 } { 2 } \left( 36 x ^ { 5 } + 8 \right) ^ { - 1 / 2 }$
B) $\frac { 1 } { 2 } \left( 6 x ^ { 6 } + 8 x \right) ^ { - 1 / 2 }$
C) $\frac { 1 } { 2 } \left( 36 x ^ { 6 } + 8 x \right) ^ { - 1 / 2 } \left( 6 x ^ { 6 } + 8 \right)$
D) $\frac { 1 } { 2 } \left( 6 x ^ { 6 } + 8 x \right) ^ { - 1 / 2 } \left( 36 x ^ { 5 } + 8 \right)$
E) $- \frac { 1 } { 2 } \left( 6 x ^ { 6 } + 8 x \right) ^ { - 3 / 2 } \left( 36 x ^ { 5 } + 8 \right)$

Question

Quizplus · Accepted Answer

To differentiate $y = \sqrt { 6 x ^ { 6 } + 8 x }$, we use the chain rule. First, rewrite the function as $y = (6x^6 + 8x)^{1/2}$. Differentiating using the chain rule gives $y' = \frac{1}{2}(6x^6 + 8x)^{-1/2} \cdot (36x^5 + 8)$, which matches option D.

Differentiate the Given Function y=6x6+8xy = \sqrt { 6 x ^ { 6 } + 8 x }y=6x6+8x​

Differentiate the Given Function $y = \sqrt { 6 x ^ { 6 } + 8 x }$