Find $\frac { \mathrm { d } } { \mathrm { du } }$ $\sqrt { u ^ { 4 } - 7 }$ .
A) $\frac { 2 u ^ { 3 } } { \sqrt { u ^ { 4 } - 7 } }$
B) $\frac { 2 u } { \sqrt { u ^ { 2 } - 7 } }$
C) $\frac { 4 u } { \sqrt { u ^ { 2 } - 7 } }$
D) $\frac { 2 u } { \sqrt { u ^ { 4 } - 7 } }$

Question

Quizplus · Accepted Answer

To differentiate $\sqrt { u ^ { 4 } - 7 }$ with respect to $u$, we use the chain rule. Let $f(u) = u^4 - 7$ and $g(f) = \sqrt{f}$. The derivative of $g(f)$ with respect to $f$ is $\frac{1}{2\sqrt{f}}$, and the derivative of $f(u)$ with respect to $u$ is $4u^3$. Applying the chain rule, we get $\frac{dg}{du} = \frac{dg}{df} \cdot \frac{df}{du} = \frac{1}{2\sqrt{u^4 - 7}} \cdot 4u^3 = \frac{2u^3}{\sqrt{u^4 - 7}}$.

Find ddu\frac { \mathrm { d } } { \mathrm { du } }dud​

Find $\frac { \mathrm { d } } { \mathrm { du } }$