CPM Homework Help : CALC Problem 6-62

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

Hint:

Use the Product Rule to find the derivative, and then derive again to find the second derivative.

Solution:

$\frac{d}{dx}=(x^2)^\prime e^x+x^2(e^x)^\prime=2xe^x+x^2e^x=e^x(2x+x^2)$