Explore the intricacies of derivatives and integrals of vector functions in this comprehensive 2-hour and 42-minute lecture. Delve into the methods for calculating derivatives and integrals of vector functions, with a particular emphasis on tangent vectors to space curves, determining tangent lines to vector functions, and solving initial value problems involving integrals. Gain a deeper understanding of these advanced calculus concepts through clear explanations and practical examples, enhancing your mathematical skills in multivariable calculus.