$\begin{array} { | r | c | c | c | c | }
\hline x & f ( x ) & f ^ { \prime } ( x ) & g ( x ) & g ^ { \prime } ( x ) \
\hline - 6 & 7 & - 8 & - 6 & 7 \
- 4 & 1 & - 5 & 0 & 5 \
- 2 & 3 & - 2 & 4 & 3 \
0 & 5 & 0 & 6 & 1 \
2 & - 5 & 1 & 6 & - 1 \
4 & - 3 & 3 & 4 & - 3 \
6 & 1 & 5 & 0 & - 5 \
\hline
\end{array}$
-Find $\frac { d } { d x } \left( g ^ { 2 } ( x ) \right) \text { when } x = 2$
A) $- 7$

B) $- 24$
C) $- 12$
D)1
E)7
F) $- 15$

G) $- 1$

H)20

Question

$\begin{array} { | r | c | c | c | c | } 
\hline x & f ( x ) & f ^ { \prime } ( x ) & g ( x ) & g ^ { \prime } ( x ) \
\hline - 6 & 7 & - 8 & - 6 & 7 \
- 4 & 1 & - 5 & 0 & 5 \
- 2 & 3 & - 2 & 4 & 3 \
0 & 5 & 0 & 6 & 1 \
2 & - 5 & 1 & 6 & - 1 \
4 & - 3 & 3 & 4 & - 3 \
6 & 1 & 5 & 0 & - 5 \
\hline
\end{array}$
-Find $\frac { d } { d x } \left( g ^ { 2 } ( x ) \right) \text { when } x = 2$
A) $- 7$

B) $- 24$
C) $- 12$
D)1
E)7
F) $- 15$

G) $- 1$

H)20

Quizplus · Accepted Answer

To find $\frac { d } { d x } \left( g ^ { 2 } ( x ) \right)$ when $x = 2$, we use the chain rule. The derivative of $g^2(x)$ with respect to $x$ is $2g(x)g'(x)$. At $x = 2$, $g(2) = 6$ and $g'(2) = -1$, so the derivative is $2 \times 6 \times (-1) = -12$.

-Find ddx(g2(x)) when x=2\frac { d } { d x } \left( g ^ { 2 } ( x ) \right) \text { when } x = 2dxd​(g2(x)) when x=2

-Find $\frac { d } { d x } \left( g ^ { 2 } ( x ) \right) \text { when } x = 2$