I've been trying to prove that if the following statement holds for all (x,y)ER^2, f must be a linear function:(adsbygoogle = window.adsbygoogle || []).push({});

f(x,y)-f(0,0)=x*(d/dx)[f(x,y)]+y*(d/dy)[f(x,y)]

It seems to work for any function I plug in, but I'm unable to establish why this always works. Also, when I say (d/dx)[f(x,y)], I mean the derivative of f(x,y) with respect to x.

Thanks in advance for any help or ideas.

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# Proof with partial derivatives

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