

IntroductionWe introduce the notion of differentiability, discuss the differentiability of standard functions and examples of nondifferentiable behavior. We then describe differentiability of a function of two variables, directional derivatives\, partial derivatives the tangent plane and the gradient. Some philosophic implications are also discussed. Topics6.1 Differentiability, the Tangent LineLinear Approximation 6.2 Differentiability of Standard Functions 6.3 Examples of non Differentiable Behavior 6.4 Derivatives in Two Dimensions: Directional Derivative and Partial Derivatives 6.5 The Tangent Plane and the Gradient Vector 