Explore the fundamentals of derivatives in this comprehensive calculus video tutorial. Learn essential concepts including the power rule, constant multiple rule, and limit definition of derivatives. Master techniques for finding tangent line slopes and differentiating various function types, including polynomial, rational, square root, radical, and trigonometric functions. Delve into advanced topics such as the product rule and quotient rule for derivatives. Apply your knowledge through numerous examples and challenge problems, gaining a solid foundation in calculus principles.