Explore the fundamental concept of derivatives in calculus through this comprehensive 30-minute video lecture. Delve into multiple definitions of derivatives using limits, and practice applying these definitions to various functions including negative exponents, square roots, and rational expressions. Learn to solve problems involving displacement and velocity, and gain proficiency in recognizing limits as derivatives without relying on L'Hôpital's Rule. Work through numerous example problems to reinforce your understanding of this crucial calculus topic.