How do you find the derivative of #f(x)=x^2e^-x#?

1 Answer
Feb 25, 2017

#f'(x)=2xe^-x-x^2e^-x#

Explanation:

differentiate using the #color(blue)"product rule"#

#"Given "f(x)=g(x).h(x)" then"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(f'(x)=g(x)h'(x)+h(x)g'(x))color(white)(2/2)|)))#

#"here "g(x)=x^2rArrg'(x)=2x#

#"and "h(x)=e^-xrArrh'(x)=e^-x.d/dx(-x)=-e^-x#

#rArrf'(x)=x^2(-e^-x)+e^-x(2x)#

#color(white)(rArrf'(x))=2xe^-x-x^2e^-x#