For differentiable vector-valued functions and

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

For differentiable vector-valued functions r(t)\mathbf r(t) and s(t)\mathbf s(t), which of the following equals ddt(r(t)⋅s(t))\displaystyle \frac{d}{dt}\big(\mathbf r(t)\cdot\mathbf s(t)\big)? (a) r′(t)⋅s′(t)\mathbf r'(t)\cdot\mathbf s'(t) (b) r′(t)⋅s(t)−r(t)⋅s′(t)\mathbf r'(t)\cdot\mathbf s(t)-\mathbf r(t)\cdot\mathbf s'(t) (c) r′(t)⋅s(t)+r(t)⋅s′(t)\mathbf r'(t)\cdot\mathbf s(t)+\mathbf r(t)\cdot\mathbf s'(t) (d) r′(t)⋅s(t)\mathbf r'(t)\cdot\mathbf s(t)

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