Differentiation Rules (Product)

Question

1. For the following exercises, assume that f(x) and g(x) are both differentiable functions with values as given in the following table. Use the following table to calculate the following derivatives.
2. Find h′(3), if h(x)=2x+f(x)g(x).

x = 1, 2, 3, 4

f(x) = 3, 5, −2, 0

g(x) = 2, 3, −4, 6

f′(x) = −1, 7, 8, −3

g′(x) = 4, 1, 2, 9

Note: The list of numbers is supposed to be a table. I tried to line everything up.

Answer 1

h(x) = 2x + f(x)g(x)

h'(x) = 2 + f'(x)g(x) + g'(x)f(x)

So, h'(3) = 2 + f'(3)g(3) + g'(3)f(3) = 2 + (8)(-4) + (2)(-2) = -34