Electrical Engineering ⇒ Topic : Laplace transform of derivative [d f(t)/dt]

 LAPLACE TRANSFORM OF A DERIVATIVE [d f(t)/dt]

                                                                ............... (1)

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

              .......... (2)

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

  ........(2a)