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How to prove the formula for L{tf(t)}?

  1. Jan 6, 2012 #1
    1. The problem statement, all variables and given/known data
    L{tf(t)} denotes the Laplace transform of tf(t). I know that it's equal to -dF(s)/ds (where F(s)=L{f(t)}) from a Laplace transform table but I don't know how to prove that.
     
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  3. Jan 6, 2012 #2

    micromass

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    What is the definition of L{tf(t)}??
     
  4. Jan 6, 2012 #3
    [tex] \int^\infty_{0} tf(t)e^{-st} dt[/tex]

    I've tried integration by parts, but it didn't help.
     
  5. Jan 6, 2012 #4

    micromass

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    OK, so I think it's best to start with

    [tex]F(s)=\int_0^\infty{f(t)e^{-ts}dt}[/tex]

    Now we wish to find [itex]F^\prime (s)[/itex]. Do you know Leibniz integral rule??
     
  6. Jan 6, 2012 #5
    No. state the rule please.
     
  7. Jan 6, 2012 #6

    micromass

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