Here is the question:

Given that:

L{Cos(9t)/sqrt(pi*t)} = e^(-9/s)/sqrt(s)

Find the laplace transformation of sqrt(t/pi)*Cos(9t)

L{sqrt(t/pi)*Cos(9t)} = ?

First I multiply the question by t/sqrt(t^2) which = 1

and question becomes

L(t * Cos(9t)/sqrt(pi*t))

so by the theorem of Differentiation of Transforms

my answer comes out to be

(-1)^1 F'(s)

= e^(-9/s)/(2e^(3/2)) - (9e^(-9/s)/s^(5/2))

But it's wrong... please tell me what I did wrong!!

Thank You!!