What is the derivative of $xe^(-kx)$ ?

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Answer 1 · 2015-06-07T15:18:58

Assuming $k$ as a constant, we can derivate this expression using product rule, which states that, be $y=f(x)g(x)$ , then $y'=f'(x)g(x)+f(x)g'(x)$ .

Naming $f(x)=x$ and $g(x)=e^(-kx)$ , we have that the derivates of these are given by: $f'(x)=1$ and $g'(x)=-ke^(-kx)$

Thus,

$(dy)/(dx)=1*e^(-kx)+x(-ke^(-kx))=color(green)(e^(-kx)(1-kx))$

What is the derivative of xe^(-kx)xe^(-kx)?