Laplace Transform of Derivatives Calculator

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Example

Created on 2024-06-20Asked by Benjamin Campbell (Solvelet student)

Find the Laplace transform of

f'(t)

given

\mathcal{L}\{f(t)\} = F(s)

Solution

The Laplace transform of a derivative is given by:

\mathcal{L}\{f'(t)\} = sF(s) - f(0)

Therefore, the Laplace transform of

f'(t)

is:

\mathcal{L}\{f'(t)\} = sF(s) - f(0)

Solved on Solvelet with Basic AI Model

Some of the related questions asked by Owen Lopez on Solvelet

1. Find the Laplace transform of the first derivative of the function

f(t) = 2e^{3t}

,2. Find the Laplace transform of the impulse response

h(t) = e^{-t}\delta(t - 2)

DefinitionDifferentiation is modified to algebraic operations in the Laplace domain. It helps in the solution of differential equations. The Laplace transform of the derivative of a function f(t), where the Laplace transform of f(t) is F(s) is L{ f ′( t )}= s F ( s )− f (0). i.e., If f(t) = eat, then the Laplace transform of f is F(s) = s−1−a. So, L{ f ′( t )}= s ⋅ s−a1− 1 = s−as−1

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