How do you differentiate f(x)=(x^-2+5x)(x^3+4) using the product rule?

1 Answer
Nov 2, 2015

f'(x) = 20x^3 + 21 - 8x^-3

Explanation:

An alternative way to solve this problem is by simplifying your equation first and avoiding the need to use the product rule.

STEP 1: Simplify by foiling
f(x) = (x^-2+5x)(x^3+4)
= x+4x^-2+5x^4+20x
= 5x^4+21x+4x^-2

STEP 2: Find the derivative using the power rule
f'(x) = 20x^3 + 21 - 8x^-3