Suppose that $h ( x ) = f ( g ( x ) )$ and $g ( 3 ) = 6$ , $g ^ { \prime } ( 3 ) = 4 ,$ $f ^ { \prime } ( 3 ) = 2 , f ^ { \prime } ( 6 ) = 7$ Find the value of $h ^ { \prime } ( 3 ) \text {. }$
A)4
B)8
C)12
D)16
E)20
F)24
G)28
H)32

Question

Quizplus · Accepted Answer

To find $h'(3)$, we use the chain rule: $h'(x) = f'(g(x)) \cdot g'(x)$. Given $g(3) = 6$ and $g'(3) = 4$, we substitute $x = 3$ into the chain rule formula. Since $f'(6) = 7$ and $g'(3) = 4$, $h'(3) = 7 \cdot 4 = 28$.

Suppose That h(x)=f(g(x))h ( x ) = f ( g ( x ) )h(x)=f(g(x))

Suppose That $h ( x ) = f ( g ( x ) )$