Laplace transforms when to use derivative? example: t(e^-t) cos3t

[datsun72]

Hi,

I have a question for laplace transforms. The example: t(e^-t) cos3t. I am trying to understand under what conditions do I do the derivative of the "s" equations? Is it when the function is multiplied like above and not added or subtracted?

Thanks so much!

 

[tkhunny]

Hi,

I have a question for laplace transforms. The example: t(e^-t) cos3t. I am trying to understand under what conditions do I do the derivative of the "s" equations? Is it when the function is multiplied like above and not added or subtracted?

Thanks so much!

It's hard to now what is wanted with so little information.

There is this:

\(\displaystyle If\;F(s)=\mathscr{L}\left\{f(t)\right\}\;and\;n\in\mathbb{N},\;then\) \(\displaystyle \mathscr{L}\left\{t^{n}f(t)\right\}=(-1)^{n}\dfrac{d^{n}}{ds^{n}}F(s).\)

So, you would "use the derivative of the "s" equation" when it is appropriate to do so. In your case, it looks like one derivative would make your life a little easier.