Laplace Transform Determination/Differentiation with Respect to Parameter

Solution Technique for Laplace Transform
To find the Laplace transform of a function $f$, one can evaluate it as follows:

Let $\map f t$ be expressible in the form:
 * $\map f t = \dfrac \d {\d a} \map g {a, t}$

Then it may be possible to express:
 * $\map {\dfrac \d {\d a} } {\laptrans {\map g {a, t} } } = \laptrans {\map {\dfrac \d {\d a} } {\map g {a, t} } }$