Explore the practical applications of derivatives in calculus through a comprehensive series of video lectures. Delve into related rates problems, optimization techniques, differentials, and Taylor polynomials. Learn to solve real-world scenarios involving changing circumferences, areas, water flow, and speed measurements. Master optimization methods for various geometric and practical situations. Understand the concept of differentials, their applications, and error propagation. Dive deep into Taylor polynomials, including their definition, coefficient determination, and error estimation. Apply these concepts through numerous examples and gain insight into Taylor's Theorem for a well-rounded understanding of derivative applications in calculus.