Question

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

Answer 1

`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`