We will use:

`Lap{t*g(t)}` `=-G^'(s)` `=-d/(ds)G(s)`

Let `g(t) = e^(-t)\ cos\ 4t`

Then

`G(s)= Lap{e^(-t)cos\ 4t}`

`=(s+1)/((s+1)^2+16)`

`=(s+1)/(s^2+2s+17)`

Now

`d/(ds)(s+1)/((s+1)^2+16)` `=-(s^2+2s-15)/((s^2+2s+17)^2)`

So `Lap{t*e^(-t)*cos\ 4t}` `=(s^2+2s-15)/((s^2+2s+17)^2)`