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

1. Jan 6, 2012

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.

2. Jan 6, 2012

### micromass

Staff Emeritus
What is the definition of L{tf(t)}??

3. Jan 6, 2012

$$\int^\infty_{0} tf(t)e^{-st} dt$$

I've tried integration by parts, but it didn't help.

4. Jan 6, 2012

### micromass

Staff Emeritus

$$F(s)=\int_0^\infty{f(t)e^{-ts}dt}$$

Now we wish to find $F^\prime (s)$. Do you know Leibniz integral rule??

5. Jan 6, 2012