# How do you differentiate (2x^2-4x+4)e^x?

May 10, 2015

for a product of functions you have the formula
$\mathmr{if} f \left(x\right) = g \left(x\right) \cdot h \left(x\right)$
$\mathmr{if} f ' \left(x\right) = g ' \left(x\right) \cdot h \left(x\right) + g \left(x\right) \cdot h ' \left(x\right)$

so lets start :)
your functions are $g \left(x\right) = 2 {x}^{2} - 4 x + 4$ and $h \left(x\right) = {e}^{x}$

so $f ' \left(x\right) = \left(4 x - 4\right) \cdot {e}^{x} + \left(2 {x}^{2} - 4 x + 4\right) \cdot {e}^{x} = \left(4 x - 4 + 2 {x}^{2} - 4 x + 4\right) \cdot {e}^{x} = 2 {x}^{2} {e}^{x}$

remember that $\frac{d}{\mathrm{dx}} {e}^{u} = {e}^{u} \cdot \frac{d}{\mathrm{dx}} u$ in this case as u=x; du/dx=1