What Is the Laplace Transform Formula for \(\mathcal{L}[f(t) \cdot g'(t)]\)?

[HWGXX7]

Hello,

I'am looking for de correct transformation formule:$$\mathcal{L}[f(t).g'(t)]$$
(and proof).

I'am not looking for method to solve it by means of integrating $$g'(t)$$, offcourse this a possible way. But assume that g(t) is much work to calculate.

So is there a good one to one formule for it?

ty&grtz

 

[HWGXX7]

Anyone an idea?

ty