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Generally if we have a function that is "common" we can find L{f(x}} and get the corresponding transform.
Example L{5} = 5/s.
You can find the table in any 2nd year book.

I would like to know how to get a Laplace transform on the Prime.
For example:
pde
∂u/∂t = 0.01 * ∂²u/∂x²

Boundary conditions:

u(0, t) = 0
u(1, t) = 200

I tried the laplace L{∂u/∂t}
expecting to get
L{∂u/∂t} = sU(x,s) - u(x,0)

BUT IN THE PRIME
laplace(∂u/∂t)

I get "X Syntax Error"

Can you get laplace transforms of derivatives?

Thank you
Anthony, Sydney