Find the derivative of function Y=`x^(2)` `e^(-x)`

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embizze | High School Teacher | (Level 1) Educator Emeritus

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We use the product rule: if f and g are differentiable functions of x then `d/(dx)(f*g)=f'g+fg'` , noting that if u is a diffeentiable function of x then `d/(dx)e^u=e^u (du)/(dx)` .

So `y=x^2e^(-x)` implies:

`y'=2xe^(-x)+x^2(-1)e^(-x)`

`=(2x-x^2)e^(-x)`

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`y'=(2x-x^2)e^(-x)`

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