Answer:
Derivative of the expression will be [tex]2e^x[/tex]
Step-by-step explanation:
We have given function [tex]y=x^2e^x-2xe^x+2e^x[/tex]
We have to fond the derivative of the expression
Let [tex]\frac{dy}{dx}=D_1-D_2+D_3[/tex] , here [tex]D_1=x^2e^x[/tex], [tex]D_2=2xe^x[/tex] and [tex]D_3=2e^x[/tex]
Now first [tex]D_1=x^2\frac{d}{dx}e^x+e^x\frac{d}{dx}x^2=x^2e^x+2xe^x[/tex]
[tex]D_2=2[x\frac{d}{dx}e^x+e^x\frac{d}{dx}x]=2xe^x+2e^x[/tex]
Now [tex]D_3=2\frac{d}{dx}e^x=2e^x[/tex]
So
[tex]D=x^2e^x+2xe^x-(2xe^x+2e^x)+2e^x=2e^x[/tex]
