Differentiation basics: Derivative f'(x) measures instantaneous rate of change. Definition: f'(a) = lim(h→0) [f(a+h) - f(a)]/h. Geometrically: Slope of tangent line at (a, f(a)). Notation: f'(x), dy/dx, Df(x) all mean derivative. Example: f(x) = x². f'(x) = lim(h→0) [(x+h)² - x²]/h = lim(h→0) [2xh + h²]/h = 2x. Rules: (1) Power: d/dx[xⁿ] = nxⁿ⁻¹; (2) Constant: d/dx[c] = 0; (3) Linear: d/dx[ax] = a. Solving: Apply definition or use rules. Shortcuts: Use derivative rules instead of limit definition for efficiency. Exam tip: Understand geometric meaning (slope). Practice both definition and rule-based approaches.