Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If $y = f ( x ) g ( x ) \text {, then } y ^ { \prime } = f ^ { \prime } ( x ) g ^ { \prime } ( x )$
A)True
B)False. The product rule is $[ f ( x ) g ( x ) ]^\prime = f ( x ) g ^ { \prime } ( x ) + g ( x ) f ^ { \prime } ( x )$

Question

Quizplus · Accepted Answer

The statement is false because the correct formula for the derivative of a product of two functions, according to the product rule, is $[ f ( x ) g ( x ) ]^\prime = f ( x ) g ^ { \prime } ( x ) + g ( x ) f ^ { \prime } ( x )$, not $f ^ { \prime } ( x ) g ^ { \prime } ( x )$.

Determine Whether the Statement Is True or False y=f(x)g(x), then y′=f′(x)g′(x)y = f ( x ) g ( x ) \text {, then } y ^ { \prime } = f ^ { \prime } ( x ) g ^ { \prime } ( x )y=f(x)g(x), then y′=f′(x)g′(x)

Determine Whether the Statement Is True or False $y = f ( x ) g ( x ) \text {, then } y ^ { \prime } = f ^ { \prime } ( x ) g ^ { \prime } ( x )$