What is dx, dy and dz in spherical coordinates

[LSMOG]

What is dx, dy and dz in spherical coordinates

 

[fresh_42]

What are $x,y,z$ in polar coordinates? Now differentiate.

 

[LSMOG]

What are $x,y,z$ in polar coordinates? Now differentiate.

Okay. Because there are many variables. x = r sinΘ cosΦ , y = r sinΘ sinΦ and z = r cos Θ, I differebtiate with respect to what variable?

 

[fresh_42]

Okay. Because there are many variables. x = r sinΘ cosΦ , y = r sinΘ sinΦ and z = r cos Θ, I differebtiate with respect to what variable?

All. There is no 1:1 correspondence. E.g. the origin is artificial in polar coordinates, e.g. $r=0$, and the angles? Then there has to be a restriction of valid intervals for the angles. We will have nine equations for (x,y,z) → (r,Θ,Φ).

 

[LSMOG]

Thanks, let me try

 

[jtbell]

In this situation, dx is the total differential of x with respect to r, θ and Φ. So look up "total differential" and see what turns up...

 

[LSMOG]

Okay. Thanks

 

[fresh_42]

You can also look up these Wikipedia pages, which cover the situation quite well:
https://en.wikipedia.org/wiki/Polar_coordinate_system#Calculus
or here where the formulas are a bit easier to see quickly:
https://de.wikipedia.org/wiki/Polarkoordinaten#Funktionaldeterminante (Fläche = area, the rest is self explaining)