Section 13.2: Derivatives and Integrals of Vector Functions

Find \(f'(2)\), where \(f(t) = \mathbf{u}(t) \cdot \mathbf{v}(t)\), \(\mathbf{u}(2) = \langle 1, 2, -1 \rangle\), \(\mathbf{u}'(2) = \langle 3, 0, 4 \rangle\), and \(\mathbf{v}(t) = \langle t, t^2, t^3 \rangle\).