Calculus Differentiation: Rules, Techniques, and Problem Solving

Differentiation is the essential tool for understanding how things change, forming the backbone of advanced mathematics, physics, and engineering. This course provides a complete, step-by-step introduction to differential calculus, equipping you with the skills to confidently calculate derivatives and use them to model and solve real-world problems. What you'll learn: * Understand the definition of the derivative using limits and fundamental continuity concepts. * Master the core rules of differentiation, including the power, product, quotient, and chain rules. * Apply implicit differentiation and related rates to solve dynamic physical and geometric scenarios. * Practice using the derivative to analyze curve behavior, determine tangents, and perform detailed curve sketching. * Configure functions for optimization problems to rigorously determine absolute maximum and minimum values. * Build proficiency in solving complex applied problems that require multiple differentiation techniques. We start with the theoretical foundation of limits and continuity, progressing quickly to the core rules and advanced techniques like the chain rule. The course emphasizes practical application through numerous worked examples and practice exercises focusing on optimization and real-world modeling. This course is designed for absolute beginners in calculus or those needing a rigorous refresher on differentiation fundamentals. No prior knowledge of calculus is required, only basic algebra skills. Start building your essential mathematical toolkit today.