How do you differentiate $(2 x^{2} - 4 x + 4) e^{x}$ $(2x^2-4x+4)e^x$ ?

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Answer 1 · 2015-05-10T07:51:05

for a product of functions you have the formula
$if f(x)=g(x)*h(x)$
$if f'(x)=g'(x)*h(x)+g(x)*h'(x)$

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

so $f'(x)=(4x-4)*e^x+(2x^2-4x+4)*e^x=(4x-4+2x^2-4x+4)*e^x=2x^2e^x$

remember that $d/dxe^u=e^u*d/dxu$ in this case as u=x; du/dx=1

How do you differentiate (2x^2-4x+4)e^x(2x2−4x+4)ex(2x^2-4x+4)e^x?