Introduction to Derivatives: Calculating Rates of Change

Are you struggling to grasp the core ideas behind calculus, especially the concept of instantaneous change? The derivative is the central concept used to measure the rate at which a function changes, forming the foundation of modern physics, engineering, and data science. This course provides a clear, foundational understanding of differentiation, enabling you to calculate rates of change, slopes of tangents, and solve optimization problems using algebraic methods. What you'll learn: * Understand the formal definition of the derivative using limits and the concept of instantaneous rate of change. * Master the fundamental differentiation rules, including the power rule, product rule, quotient rule, and the essential chain rule. * Practice calculating derivatives for common function types, including polynomial, trigonometric, exponential, and logarithmic functions. * Apply derivatives to solve practical problems involving related rates, curve sketching, and optimization (finding maximum and minimum values). * Learn to use implicit differentiation and calculate higher-order derivatives. * Define the connection between differentiation and basic integration concepts (antiderivatives). The course begins by defining limits and the derivative, then systematically introduces the essential rules and techniques needed to differentiate complex functions, concluding with key applications. All concepts are explained clearly through written examples and guided practice exercises. This course is designed for absolute beginners with a basic understanding of algebra and functions. No prior experience with calculus or advanced mathematics is required. Start building your essential calculus foundation today.