Suppose that $F(x)=f(g(x))$ and $g(14)=2$ , $g^{\prime}(14)=5$ , $f^{\prime}(14)=15$ , and $f^{\prime}(2)=16$ . Find $F^{\prime}(14)$ .
A) 20
B) $80$
C) 24
D) 140
E) 17

Name: Suppose that $F(x)=f(g(x))$ and $g(14)=2$ , $g^{\prime}(14)=5$ , $f^{\prime}(14)=15$ , and $f^{\prime}(2)=16$ . Find $F^{\prime}(14)$ . A) 20 B) $80$ C) 24 D) 140 E) 17
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Question

Quizplus · Accepted Answer

Using the chain rule, $F'(x) = f'(g(x)) \cdot g'(x)$. Substituting the given values: $F'(14) = f'(g(14)) \cdot g'(14) = f'(2) \cdot 5 = 16 \cdot 5 = 80$.

Suppose That F(x)=f(g(x))F(x)=f(g(x))F(x)=f(g(x)) And g(14)=2g(14)=2g(14)=2 g′(14)=5g^{\prime}(14)=5g′(14)=5 f′(14)=15f^{\prime}(14)=15f′(14)=15 , And f′(2)=16f^{\prime}(2)=16f′(2)=16 Find F′(14)F^{\prime}(14)F′(14) A) 20 B)

Suppose That $F(x)=f(g(x))$ And $g(14)=2$ $g^{\prime}(14)=5$ $f^{\prime}(14)=15$ , And $f^{\prime}(2)=16$ Find $F^{\prime}(14)$
A) 20
B)