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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

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# Partial Differentiation, complication in variables held constant

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