Suppose that the functions f and g and their derivatives with respect to x have the following values at the given values of
x. Find the derivative with respect to x of the given combination at the given value of x.
-

$\sqrt { f ( x ) + g ( x ) } , x = 3$
A) $\frac { 1 } { 2 \sqrt { 17 } }$
B) $\frac { 13 } { \sqrt { 17 } }$
C) $- \frac { 1 } { 2 \sqrt { 17 } }$
D) $\frac { 13 } { 2 \sqrt { 17 } }$

Question

Suppose that the functions f and g and their derivatives with respect to x have the following values at the given values of
x. Find the derivative with respect to x of the given combination at the given value of x.
-

$\sqrt { f ( x ) + g ( x ) } , x = 3$
A) $\frac { 1 } { 2 \sqrt { 17 } }$ 
B) $\frac { 13 } { \sqrt { 17 } }$ 
C) $- \frac { 1 } { 2 \sqrt { 17 } }$ 
D) $\frac { 13 } { 2 \sqrt { 17 } }$

Quizplus · Accepted Answer

Using the chain rule and the given values, we have

\begin{align*}
\frac { d } { dx } \sqrt { f ( x ) + g ( x ) } \bigg|_{x=3} &= \frac{1}{2 \sqrt{f(3)+g(3)}}\cdot \frac{d}{dx} (f(x)+g(x))\bigg|_{x=3} \
&= \frac{1}{2 \sqrt{f(3)+g(3)}}\cdot (f'(3)+g'(3)) \
&= \frac{1}{2 \sqrt{27+10}}\cdot (6+7) \
&= \frac{13}{2 \sqrt{37}} \
&= \frac{13\sqrt{37}}{74}
\end{align*}

So the answer is D.

Suppose That the Functions F and G and Their Derivatives f(x)+g(x),x=3\sqrt { f ( x ) + g ( x ) } , x = 3f(x)+g(x)​,x=3

Suppose That the Functions F and G and Their Derivatives $\sqrt { f ( x ) + g ( x ) } , x = 3$