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OCW Scholar - Multivariable Calculus
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On http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/part-c-parametric-equations-for-curves/session-21-keplers-second-law/MIT18_02SC_MNotes_k.pdf : Middle of Page 1, under "1. Differentiation of Products of Vectors." In the second way of proving the product rule, it says "Let t increase by /Delta t. Then r increases by /delta r, and s by/delta s, and the corresponding change in r (dot) s is given by /delta r (dot) s =(r+\delta r) (dot) (s+\delta s) - r (dot) s. ..." My question is where is the "\delta r (dot) s=..." equation from, how was it derived?
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this seems pretty obvious Δ(r⋅s)=(r+Δr)⋅(s+Δs)−r⋅s = Δr.s + r.Δs + Δr.Δs since Δr.Δs is very small ... i guess it get's ignored.
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