CPM Homework Help : APCALC Problem 6-62

What is $\frac { d ^ { 2 } } { d x ^ { 2 } } [ x ^ { 2 } e ^ { x } ]$ ? Remember that $\frac { d ^ { 2 } y } { d x ^ { 2 } }$ denotes the second derivative. Simplify your result.

Hint:

Use the Product Rule to obtain the first derivative, and then take the derivative of it to obtain the second derivative.

Solution:

$\frac { d ^ { 2 } y } { d x ^ { 2 } }= e^x(2+4x+x^2)$