Hello there, my first time so if it's in bad category please move it where it belongs

In short, I need to create normals for wave, so I use derivative of wave and then make line perpedicular to it. I found that I can make perpedicular using this formula:

I need to find perpediculars for derivated wave function. And now that's where problem begins. My wave function:

I have very little knoweledge about derivative, I'm not on university yet and most of what I know is through searching net.. I think I can derivate first function, but second with 2 parameters does real problem. I already tried solve it (found something about partial derivatives on wikipedia), and as I make graphical computation I can compare results and it was not really like solution I'm sure about. So I think I got lost there somewhere derivating G...

I would be glad if someone could solve this one a show me steps also not just solution, so I can learn from it.

Thanks in advance