Derivatives

Average and instantaneous velocity, The derivative at a point: the limit definition, The tangent line, The derivative function, Interpreting the derivative: rates and units, The second derivative, concavity and acceleration, Differentiability and continuity, Local linearization, The power, constant multiple and sum rules, Derivatives of exponential functions, Derivatives of sine and cosine, The product rule, The quotient rule, Derivatives of tangent, secant, cotangent and cosecant, The chain rule, Derivatives of inverse functions: ln x, arcsin x, arctan x, Implicit differentiation, Tangent lines to curves defined implicitly, The derivative of an inverse function, Related rates: area and volume, Related rates with right triangles, Related rates with similar triangles, L'Hôpital's rule, Critical numbers and the first derivative test, The second derivative test and inflection points, Global extrema on a closed interval, The Mean Value Theorem, Motion on a line: velocity, acceleration, distance, Optimization