Suppose that $F ( x ) = f ( g ( x ) )$ and $g ( 14 ) = 2 , g ^ { \prime } ( 14 ) = 4 , f ^ { \prime } ( 14 ) = 15$, and $f ^ { \prime } ( 2 ) = 13$. Find $F ^ { \prime } ( 14 )$.
A) 140
B) 20
C) 24
D) 52
E) 17

Question

Quizplus · Accepted Answer

To find $F'(14)$, we use the chain rule: $F'(x) = f'(g(x)) \cdot g'(x)$. Given $g(14) = 2$, $g'(14) = 4$, and $f'(2) = 13$, we substitute these values to get $F'(14) = 13 \cdot 4 = 52$.

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

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