Hi,(adsbygoogle = window.adsbygoogle || []).push({});

this is a pretty trivial question. would be grateful if someone could answer it for me.

in spherical polars x=rcos(theta)sin(PHI) and so on for y, and z

Now, why is

d/dr= dx/dr*d/dx + dy/dr*d/dy+ dz/dr*d/dz

where everything is partial. dx/dr, dy/dr and dz/dr at partial derivates held at contant thetha and phi.

why are they held at constant thetha and phi?

r^2=x^2 + y^2 + z^2

so r=function of (x,y,z)

thus we can write this out as an exact differential we get:

dr=dr/dx*dr + dr/dy*dy + dr/dz*dz

dr/dx is held constant wrt y,z etc. and NOT thetha and phi.

Can some explain how the differential at the top works.

thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Partial Differentiation, complication in variables held constant

**Physics Forums | Science Articles, Homework Help, Discussion**