Detail solution
-
Apply the product rule:
; to find :
-
Apply the power rule: goes to
; to find :
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The derivative of is itself.
The result is:
-
Now simplify:
The answer is:
The first derivative
[src]
$$x^{3} e^{x} + 3 x^{2} e^{x}$$
The second derivative
[src]
/ 2 \ x
x*\6 + x + 6*x/*e
$$x \left(x^{2} + 6 x + 6\right) e^{x}$$
The third derivative
[src]
/ 3 2 \ x
\6 + x + 9*x + 18*x/*e
$$\left(x^{3} + 9 x^{2} + 18 x + 6\right) e^{x}$$