Calculus: Derivative and Differential Techniques

What is a derivative? At its heart, a derivative is simply the slope of a tangent line at a specific point on a curve. In this video, we move from the "First Principles" definition to the professional shortcuts used to differentiate complex functions in seconds. Key Highlights of this Lesson: • The Limit Definition: How f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} defines the instantaneous rate of change. • The Power Rule: The fastest way to differentiate polynomials (nx^{n-1}). • Product & Quotient Rules: Mastering the math when functions are multiplied or divided. • Trigonometric & Exponential Derivatives: Why the derivative of e^x is the most unique function in math. • The Chain Rule: The essential "Outside-In" technique for differentiating composite functions like \sin(x^2).