Given and , determine at…

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

Problem

Given r(t)=⟨t,t2,1⟩r(t)=\langle t, t^{2}, 1\rangle and s(t)=⟨cos⁡t,sin⁡t,t⟩s(t)=\langle \cos t, \sin t, t\rangle, determine ddt(r(t)⋅s(t))\displaystyle \frac{d}{dt}\big(r(t)\cdot s(t)\big) at t=πt=\pi.

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