Laplace Transform of the Derivative

Suppose that the Laplace transform of y(t) is Y(s). Then the Laplace

Transform of y'(t) is

For the second derivative we have

For the n'th derivative we have

Reference:

http://www.math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/ode/laplace/lt/lt.html