Answer:
-27e^(-2).
= -3.654 to 3 decimal places.
Explanation:
d/dx((3x^2 + 3)e^-x)
Using the Product Rule:
Derivative = (3x^2 + 3) d/dx(e^-x) + e^-x d/dx(3x^2 + 3)
= -e^-x(3x^2 + 3) + e^-x(6x)
= e^-x(6x -1*(3x^2 + 3))
= e^-x(6x - 3x^2 - 3)
= 3e^-x(2x - x^2 - 1)
= -3e^-x(x^2 - 2x + 1)
= -3e^-x(x - 1)^2
When x = -2,
Derivative = -3e^(-2)(-2-1)^2
= -27e^(-2)