Let's say I have two vector fields(adsbygoogle = window.adsbygoogle || []).push({}); a(x,y,z) andb(x,y,z).

Let's say I have a scalar field f equal toa•b.

I want to find a clean-looking, simple way to express the directional derivative of this dot product alonga, considering only changes inb.

Ideally, I would like to be able to express this without invoking unit vectors and without || 's, while still using vector notation.

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# I A directional, partial derivative of a scalar product?

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