Question

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

Answer 1

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))`