# Solving Laplace Eqn by Separation of vbls

Okay, I'm stumped at what seems like a very simple mathematical step

Then, the next step is

I see what changed, but I don't understand exactly what happened. Can someone please explain? Thanks in advance!

Born2bwire
$$\frac{\partial}{\partial x} \left(f(x)g(x)\right) = g(x) \frac{\partial f(x)}{\partial x} + f(x) \frac{\partial g(x)}{\partial x}$$