Question

Suppose that

f(5) = 1,
f '(5) = 8,
g(5) = −2,
g'(5) = 5.
Find the following value
(a) (fg)'(5)

Answer 1

To find the value of (fg)'(5), use the product rule for differentiation. (fg)'(5) = -11.

Step-by-step explanation:

To find the value of (fg)'(5), we need to use the product rule for differentiation. The product rule states that (fg)' = f'g + fg'.

In this case, f(5) = 1, f'(5) = 8, g(5) = -2, and g'(5) = 5.

Using the product rule, we can calculate (fg)'(5) as follows:

1. Calculate f'g: f'(5) * g(5) = 8 * (-2) = -16.
2. Calculate fg': f(5) * g'(5) = 1 * 5 = 5.
3. Add the two results together: (fg)'(5) = f'g + fg' = -16 + 5 = -11.

Therefore, (fg)'(5) = -11.