Derivatives: Definition and Properties

This lecture covers the definition and properties of derivatives, focusing on the slopes of tangent lines and the concept of differentiability. It explains the left and right derivatives, as well as the conditions for a function to be differentiable. The lecture also discusses the slopes of half-tangent lines and the concept of divisibility on the left and right. Moreover, it explores the limits of functions and the slopes of semi-tangent lines, providing a comprehensive overview of the fundamental principles of derivatives.