Distance equations for different cord. systems

1. Sep 25, 2006

aquabug918

I need to show that

ds^2 = dx^ + dy^2 + dz^2

is the same as

ds^2 = dr^2 + r^2 (dpheta^2 + sin^2pheta*dphi^2)

.... I know that I need to use x = r sin pheta cos phi
y = r sin pheta sin phi
z = r cos pheta

I am confused but I think I have to take the derivitive of something. Do I somehow take the partial derivitives and if so of what? Can someone point me in the right direction. Thank you!

2. Sep 25, 2006

AKG

In general, I believe if you have a function f of several variables x1, ..., xn, then:

$$df = \sum _{k=1} ^n\frac{\partial f}{\partial x_k}dx_k$$

3. Sep 25, 2006

AKG

Do Not Post The Same Question Twice

4. Sep 25, 2006

StatusX

dx=$\partial x /\partial r dr + \partial x /\partial \theta d\theta + \partial x /\partial \phi d\phi$, and likewise for y and z. Plug in and simplify.