Use the given information to find $f ^ { \prime } ( 2 )$ of the function $f ( x ) = g ( x ) h ( x )$ . $g ( 2 ) = 3 \text { and } g ^ { \prime } ( 2 ) = - 2 , h ( 2 ) = - 1 \text { and } h ^ { \prime } ( 2 ) = 4$
A) $f ^ { \prime } ( 2 ) = 14$
B) $f ^ { \prime } ( 2 ) = - 11$
C) $f ^ { \prime } ( 2 ) = 17$
D) $f ^ { \prime } ( 2 ) = - 9$
E) $f ^ { \prime } ( 2 ) = 12$

Question

Quizplus · Accepted Answer

Using the product rule, we have:$$f'(x) = g(x)h'(x) + g'(x)h(x)$$Substituting the given values, we get:$$f'(2) = g(2)h'(2) + g'(2)h(2)$$$$f'(2) = 3(4) + (-2)(-1)$$$$f'(2) = 12 + 2$$$$f'(2) = 14$$

Use the Given Information to Find f′(2)f ^ { \prime } ( 2 )f′(2)

Use the Given Information to Find $f ^ { \prime } ( 2 )$