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I don't understand the following.

I have this function: [tex]V(x,y,z)=\frac{(A+B+C)r^2-3(Ax^2+By^2+Cz^2)}{r^5}[/tex] with [itex]r=\sqrt{x^2+y^2+z^2}[/itex]

and on the textbook they say that if x,y,z are approximately equal or comparable as order of magnitude to r, and if they are all "big" enough (they are indeed tens of thousands od kilometers), one can approximate the partial derivatives of V with respect to x, y and z, with the partial derivative of the numerator alone. I can compute both derivatives but still I don't see them as approximatively equal. Should i try with spherical coordinates? However it should be clear in cartesian coordinates too, I think...

Could someone please show me this fact? It is a pretty important point in the chapter and everybody just says this is true because we are talking about orders of magnitude...

Thank you in advance

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# How is this a good approximation?

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