Let f(t) be a function with L[f](s) = F(s). Use the fact that L[(t^n)f(t)] = ((-1)^n)*F^(n)(s) to show that L[t*f'(t)](s)=-s*F'(s) - F(s).
A proof with the frequency differentiation property of Laplace Transforms is provided. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.