How do you find the derivative of # x^2 * e^-x#?

1 Answer
Jun 15, 2016

#d/dx(x^2*e^-x)=2xe^-x-x^2e^-x#

Explanation:

This problem requires use of the product rule, which states:
#d/dx(uv)=u'v+uv'#
Where #u# and #v# are functions of #x#.

In our case, #u=x^2->u'=2x# and #v=e^(-x)->v'=-e^(-x)#. Thus
#d/dx(x^2*e^-x)=(2x)(e^-x)+(x^2)(-e^-x)#
#=2xe^-x-x^2e^-x#

We could simplify this a little further by, say, pulling out an #xe^-x#:
#d/dx(x^2*e^-x)=xe^-x(2-x)#

Either form is correct.