Derivative of a multiple of Heaviside step function

Question

First of all, thanks for your time, I have a question. Let's assume that we have: f(x)=(Heaviside's step function)*e^(3x) Now let's assume to calculate the derivate of this function, why we have this:

The derivative of this function must be: dirac*e^(3x)+ 3*e^(3x), but my book and Wolfram Alpha says that this is incorrect. Why have weonly dirac+3*e^(3x)?

Answer 1

$\delta(x) = \delta(x) e^{3x}$ for all $x$.

This is because $e^{3x}$ evaluated at $x=0$ is $1$.