Detail solution
-
Apply the product rule:
; to find :
-
Apply the power rule: goes to
; to find :
-
The derivative of is itself.
The result is:
-
Now simplify:
The answer is:
The first derivative
[src]
$$x^{2} e^{x} + 2 x e^{x}$$
The second derivative
[src]
$$\left(x^{2} + 4 x + 2\right) e^{x}$$
The third derivative
[src]
$$\left(x^{2} + 6 x + 6\right) e^{x}$$