# Laplace transform

#### idontknow

How can I find the n-th derivative of laplace integral ?

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#### DarnItJimImAnEngineer

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 $$\displaystyle s^nF(s) + s^{n-1}f(0) + s^{n-2}f'(0) + s^{n-2}f''(0) + â€¦ + f^{(n-1)}(0)$$.

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