Problem

Let f(x) = x² and g(x) = x. Find (f + g)' (4). Does this equal f '(4) + g'(4)?

Solution

Using the power rule, we can figure out f '(x) and g'(x).

Therefore f '(4) = 2 ^. 4 = 8, and g'(4) = 1, so f '(4) + g'(4) = 8 + 1 = 9.

Next, we'll compute (f + g)' (4) using the definition of the derivative.

Therefore (f + g)' (4) equals f '(4) + g'(4).