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

1 Answer
Jim G.
Mar 12, 2017

#f'(x)=-e^x(x+1)#

Explanation:

differentiate #xe^x# using the #color(blue)"product rule"#

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

#• dy/dx=g(x)h'(x)+h(x)g'(x)#

#"here "g(x)=xrArrg'(x)=1#

#"and "h(x)=e^xrArrh'(x)=e^x#

#rArrf(x)=-xe^x+2#

#rArrf'(x)=-(x.e^x+e^x)+0=-xe^x-e^x#

#color(white)(rArrf'(x))=-e^x(x+1)#

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