Define , , and . Determine when…

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

Problem

Define v(t)=t2+1v(t)=t^{2}+1, u(v)=v3u(v)=v^{3}, and r(u)=⟨ucos⁡u, ln⁡(1+u2)⟩\mathbf r(u)=\langle u\cos u,\,\ln(1+u^{2})\rangle. Determine drdt\dfrac{d\mathbf r}{dt} when t=1t=1.

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