Electrical Engineering ⇒ Topic : Laplace transform of derivative [d f(t)/dt]
LAPLACE TRANSFORM OF A DERIVATIVE [d f(t)/dt]
Therefore, the Laplace transform of the first-derivative of a time function f(t) is s times the Laplace transform of f(t) minus the limit of f (t) as t → 0+.
In general, we can write
To apply Laplace transformation in circuit theory, the time t = 0 is considered as closing the switch. For initial condition the time t = 0- is considered. Therefore, Eq. (2) becomes
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