This lesson teaches students how to find the derivatives and integrals of vector functions, along with several applications, such as finding the equation of a tangent line, finding second derivatives, and determining if a curve is smooth. In addition, students learn to produce basic proofs using the rules of differentiation and integration. This lesson is meant for a Multivariable Calculus course, but it could be used after AP Calculus exams have finished. Detailed answer keys are included. Th