do we use the product rule here Its a bit confusing because

do we use the product rule here? Its a bit confusing because it looks like product, and i can just solve it by for example..

(6x-6)e^x, but I highly doubt that is the answer

Solution

f(x) = (3x² -6x +6)e^x

f \'(x) = [3(2x) -6 + 0]e^x + (3x² -6x +6)e^x          since d/dx xⁿ = nx^n-1 ; (uv)\' = u\'v + uv\' ; d/dx e^x = e^x

==> f \'(x) = [6x -6]e^x + (3x² -6x +6)e^x

==> f \'(x) = 6xe^x -6e^x + 3x²e^x -6xe^x +6e^x

==> f \'(x) = 3x²e^x