Section 13.2: Derivatives and Integrals of Vector Functions

If \(\mathbf{u}(t) = \langle \sin t, \cos t, t \rangle\) and \(\mathbf{v}(t) = \langle t, \cos t, \sin t \rangle\), use Formula 4 of Theorem 3 to find \(\frac{d}{dt}[\mathbf{u}(t) \cdot \mathbf{v}(t)]\)