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

Apr 25, 2018

$f ' \left(x\right) = \left(5 {e}^{x} + {\sec}^{2} x\right) \left({x}^{2} - 2 x\right) + \left(5 {e}^{x} + \tan x\right) \left(2 x - 2\right)$
For $f \left(x\right) = \left(5 {e}^{x} + \tan x\right) \left({x}^{2} - 2 x\right)$, we find $f ' \left(x\right)$ by doing:
$f ' \left(x\right) = \frac{d}{\mathrm{dx}} \left[5 {e}^{x} + \tan x\right] \left({x}^{2} - 2 x\right) + \left(5 {e}^{x} + \tan x\right) \frac{d}{\mathrm{dx}} \left[{x}^{2} - 2 x\right]$
$f ' \left(x\right) = \left(5 {e}^{x} + {\sec}^{2} x\right) \left({x}^{2} - 2 x\right) + \left(5 {e}^{x} + \tan x\right) \left(2 x - 2\right)$