Deriving laplace transform

Question

Assignment:

A.) Using the knowledge that the Laplace transform of dX/dt is sX(s) and:

dV_out / dt  = 1/RC (V_in - V_out)

derive the Laplace transform of the above system, Vout(s)/Vin(s).

B.) Using the knowledge that the Laplace transform for C is 1/(sC) and that the Laplace Transform of R is simply R, re-derive the transfer function for the above circuit, Vout(s)/Vin(s), with the differential equation found as the starting point. (The answer should be the same as A)

C.) Given the results of 12, and the knowledge that the Laplace transform of a unit step is 1/s, calculate the Laplace transform Vout(s) for Vin=unit step.