Use the Product Rule to find the derivative of the function. A)4x² + 16 B)4x C)2x + 2

Question

Quizplus · Accepted Answer

The Product Rule states that if f(x) and g(x) are two functions, then the derivative of their product f(x)g(x) is given by f'(x)g(x) + g'(x)f(x). In this case, let f(x) = 11eaa3e5_55ff_ff52_9f8f_65c4db6453d3_TB5971_11 and g(x) = x. Then, f'(x) = 0 (since 11eaa3e5_55ff_ff52_9f8f_65c4db6453d3_TB5971_11 is a constant) and g'(x) = 1. Thus, applying the Product Rule, we have:

(fg)'(x) = f'(x)g(x) + g'(x)f(x)
= 0(x) + 1(11eaa3e5_55ff_ff52_9f8f_65c4db6453d3_TB5971_11)
= 11eaa3e5_55ff_ff52_9f8f_65c4db6453d3_TB5971_11

Therefore, the derivative of the given function is 11eaa3e5_55ff_ff52_9f8f_65c4db6453d3_TB5971_11, which corresponds to choice D.

Use the Product Rule to Find the Derivative of the Function