Answer:
the question is incomplete, the complete question is "find the derivative of the function [tex]y=3e^{x}-xe^{x}[/tex]"
answer: [tex]\frac{dy}{dx}=(2-x)e^{x}[/tex].
Step-by-step explanation:
From the equation, [tex]y=3e^{x}-xe^{x}[/tex], we approach the question using the differentiation of a product and differentiation of a sum simultaneously,
the differentiation of a sum is express as
f(x)=u(x)+v(x)+.....w(x) then
[tex]\frac{df(x)}{dx}=\frac{du(x)}{dx}+\frac{dv(x)}{dx}+...\frac{dw(x)}{dx}.\\[/tex]
For the differentiation of a product we have
f(x)=u(x)v(x), then
[tex]\frac{df(x)}{dx}=\frac{dv(x)}{dx}u(x)+\frac{du(x)}{dx}v(x)[/tex]
hence if we go by the formula we arrive at
for [tex]y=3e^{x}[/tex]
let u(x)=3 hence du/dx=0 and
[tex]v(x)=e^{x}[/tex] and [tex]\frac{dv(x)}{dx}=e^{x}[/tex]
hence [tex]\frac{dy}{dx}=3e^{x}+0e^{x}\\\frac{dy}{dx}=3e^{x}---equation 1\\[/tex]
Also for [tex]y=-xe^{x}\\\frac{dy}{dx}=-e^{x}-xe^{x}---equation 2[/tex].
if we add equation 1 and equation 2 we arrive at
[tex]\frac{dy}{dx}=3e^{x}-e^{x}-xe^{x}\\\frac{dy}{dx}=(3-1-x)e^{x}\\\frac{dy}{dx}=(2-x)e^{x}[/tex].
