How do you differentiate f(x)= e^(3x) * (5x^2-x+1)^12 using the product rule?

$f ' \left(x\right) = 12 {e}^{3 x} \left(10 x - 1\right) {\left(5 {x}^{2} - x + 1\right)}^{11} + 3 {e}^{3 x} {\left(5 {x}^{2} - x + 1\right)}^{12}$
$f = {e}^{3 x} , g = {\left(5 {x}^{2} - x + 1\right)}^{12}$
$f ' = {e}^{3 x} \cdot 3 = 3 {e}^{3 x} , g ' = 12 {\left(5 {x}^{2} - x + 1\right)}^{11} \cdot \left(10 x - 1\right)$
$f ' \left(x\right) = f g ' + g f '$
$f ' \left(x\right) = 12 {e}^{3 x} \left(10 x - 1\right) {\left(5 {x}^{2} - x + 1\right)}^{11} + 3 {e}^{3 x} {\left(5 {x}^{2} - x + 1\right)}^{12}$