Laplace differentiation question

[kris]

Hi I'm learning laplace transform, specifically multiplying by 't' and 't^n'. Now i understand the concept that L{tf(t)} = -F'(s) but I'm confused with the differentiation part of the process (having a bit of a dim moment!).

Here is the example it gives:

L{sin2t} = 2 / (s^2 + 4), therefore L{tsin2t} = -d/ds(2 / (s^2 +4)) = 4s / (s^2 + 4)^2

the differentiation at the end is the bit that is confusing me i.e. how to do it. I know this should be the simple bit but it completely evades my understanding at this point .

Any help would be appreciated

thanks

 

[mathman]

I'll assume you know how to differentiate. Let u=s²+4.
d/ds(2/u)=-(2/u²)du/ds. du/ds=2s. Just put it all together.