Finding derivatives from a table Find the values of the following derivatives using the table. <IMAGE>


c. d/dx ((f(x)g(x)) |x=3

Verified step by step guidance

1. Step 1: Recall the product rule for derivatives, which states that if you have two functions f(x) and g(x), the derivative of their product is given by (f(x)g(x))' = f'(x)g(x) + f(x)g'(x).
2. Step 2: Identify the values you need from the table. You will need f(3), g(3), f'(3), and g'(3) to apply the product rule at x = 3.
3. Step 3: Substitute the values from the table into the product rule formula. This means replacing f(x) with f(3), g(x) with g(3), f'(x) with f'(3), and g'(x) with g'(3).
4. Step 4: Calculate each term separately. First, compute f'(3)g(3) and then f(3)g'(3).
5. Step 5: Add the results from Step 4 to find the derivative of the product at x = 3.