If and , use Formula 4 of Theorem 3 to find d dt [ u (t) v…

MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

\mathbf{u}(t) = \langle \sin t, \cos t, t \rangle

and

\mathbf{v}(t) = \langle t, \cos t, \sin t \rangle

, use Formula 4 of Theorem 3 to find

\frac{d}{dt} [\mathbf{u}(t) \cdot \mathbf{v}(t)]