$\begin{array} { | l | l | l | l | l | }
\hline \mathrm { X } & \mathrm { g } ( \mathrm { x } ) & \mathrm { h } ( \mathrm { x } ) & \mathrm { g } ^ { \prime } ( \mathrm { x } ) & \mathrm { h } ^ { \prime } ( \mathrm { x } ) \
\hline - 3 & 0 & 3 & 1 & 0 \
\hline - 2 & 1 & 2 & 2 & - 3 \
\hline - 1 & 3 & 0 & - 1 & - 2 \
\hline 0 & 2 & 3 & - 2 & 3 \
\hline 1 & 0 & - 1 & - 2 & - 2 \
\hline 2 & - 2 & - 2 & - 1 & 0 \
\hline 3 & - 3 & 0 & 0 & 1 \
\hline
\end{array}$
-Use the table above to find $f ^ { \prime } ( - 2 )$ if $f ( x ) = g ( h ( x ) )$
A) - 3
B) 3
C) - 1
D) 1

Question

$\begin{array} { | l | l | l | l | l | } 
\hline \mathrm { X } & \mathrm { g } ( \mathrm { x } ) & \mathrm { h } ( \mathrm { x } ) & \mathrm { g } ^ { \prime } ( \mathrm { x } ) & \mathrm { h } ^ { \prime } ( \mathrm { x } ) \
\hline - 3 & 0 & 3 & 1 & 0 \
\hline - 2 & 1 & 2 & 2 & - 3 \
\hline - 1 & 3 & 0 & - 1 & - 2 \
\hline 0 & 2 & 3 & - 2 & 3 \
\hline 1 & 0 & - 1 & - 2 & - 2 \
\hline 2 & - 2 & - 2 & - 1 & 0 \
\hline 3 & - 3 & 0 & 0 & 1 \
\hline
\end{array}$
-Use the table above to find $f ^ { \prime } ( - 2 )$ if $f ( x ) = g ( h ( x ) )$
A) - 3
B) 3
C) - 1
D) 1

Quizplus · Accepted Answer

To find $f'(x)$ when $f(x) = g(h(x))$, we use the chain rule: $f'(x) = g'(h(x)) \cdot h'(x)$. For $x = -2$, $h(-2) = 2$ and $h'(-2) = -3$. Looking up $g'(2) = -1$, we get $f'(-2) = g'(h(-2)) \cdot h'(-2) = (-1) \cdot (-3) = 3$.

-Use the Table Above to Find f′(−2)f ^ { \prime } ( - 2 )f′(−2)

-Use the Table Above to Find $f ^ { \prime } ( - 2 )$