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

Nov 2, 2015

#### Answer:

$f ' \left(x\right) = 20 {x}^{3} + 21 - 8 {x}^{-} 3$

#### 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
$f \left(x\right) = \left({x}^{-} 2 + 5 x\right) \left({x}^{3} + 4\right)$
$= x + 4 {x}^{-} 2 + 5 {x}^{4} + 20 x$
$= 5 {x}^{4} + 21 x + 4 {x}^{-} 2$

STEP 2: Find the derivative using the power rule
$f ' \left(x\right) = 20 {x}^{3} + 21 - 8 {x}^{-} 3$