# Where does the linearity of differential operators come from?

I just quoted the linearity of a differential operator, namely d/dz, in a proof and I was wondering where the root of this linearity lies. All of the differential operators which I have encountered seem to be linear and the 'sketch' derivation in my Vector Calculus course for higher dimensional derivatives used a linear mapping approach.

My question is, where does this linearity appear and how does it fit in with the natural 'rates of change' intuition of derivatives?

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