Laplace transform

Dec 2015
973
128
Earth
How can I find the n-th derivative of laplace integral ?
 
Last edited:
Jun 2019
493
262
USA
Do you mean the Laplace transform of \(\displaystyle \frac{d^nf}{dt^2}\)?
If \(\displaystyle f(t)\mapsto F(s)\), then \(\displaystyle f^{(n)}(t) \mapsto s^nF(s)\) if \(\displaystyle f(t)=0 ~\forall~ t<0\) (such as a step, ramp, etc.). In the general case, it maps to \(\displaystyle s^nF(s) + s^{n-1}f(0) + s^{n-2}f'(0) + s^{n-2}f''(0) + … + f^{(n-1)}(0)\).
 
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