Question

quiz 00 (id 780232)
due: thu jan 22 23:59 2026. until due: 0.1 days.
restart = 0, attempt 1.
question number 1. (4.00 points)
\\(\frac{d}{dx}\left(f(x)\cdot g(x)\
ight)=\\)
\\(\circ f(x)g(x)-f(x)g(x)\\)
\\(\circ f(x)g(x)\\)
\\(\circ f(x)g(x)+f(x)g(x)\\)
\\(\circ g(x)+f(x)\\)
\\(\circ\\)none of the above
question number 2. (4.00 points)

Explanation:

The problem is about finding the derivative of the product of two functions \( f(x) \) and \( g(x) \). By the product rule in calculus, the derivative of \( f(x) \cdot g(x) \) with respect to \( x \) is \( f(x)g'(x)+f'(x)g(x) \). We check the options: the first option is the quotient rule (or negative of product rule's sign error), the second is wrong (derivative of product is not product of derivatives), the fourth is derivative of sum, and the third option matches the product rule.

Answer:

\( f(x) g'(x) + f'(x) g(x) \) (the third option among the given choices)