Proof - Express in Clyndrical Coordinates

[forestmine]

Proof -- Express in Clyndrical Coordinates

Homework Statement

Show that when you express ds^2 = dx^2 + dy^2 +dz^2 in cylindrical coordinates, you get ds^2 = dr^2 + r^2d^2 + dz^2.

Homework Equations

x=rcosθ
y=rsinθ
z=z

The Attempt at a Solution

EDIT// I was really over thinking this...think I've got it figured out. Thanks anyways!

I'm somewhat confused about the notation here and how to really go about this. My first thought was just to plug in some values...

ds^2 = d(r^2*cos^2(θ)) + d(r^2*sin^2(θ)) + dz^2

The d(__) are really throwing me off here. I don't see how the second term in the right hand side of the proof goes to r^2d^2.

Ah really lost here. Just need some help in the right direction.

Thank you!

 

[Muphrid]

You should interpret dx^2 as meaning (dx)^2.

 

[forestmine]

I think that was my hang up exactly. Thanks!