We derive the formula for the Laplace transform of df/dt in terms of that for f(t) and f(0). It is then shown how to extrapolate the rule to write down the transforms for 2nd, 3rd and higher derivatives.

Laplace transform of the derivative of a function (MathsCasts)

These MathsCasts were produced by the mathematics support centres at Swinburne University, the University of Limerick and Loughborough University. They were part of a collaborative research project to develop high quality resources and investigate the effectiveness of MathsCasts to support mathematics learning. The full set of resources are available at http://commons.swin.edu.au/s/mathscasts MathsCasts are licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License

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Laplace transform of the derivative of a function (MathsCasts)

Laplace transform of the derivative of a function (MathsCasts)