We introduce the notion of differentiability, discuss the differentiability of standard functions and examples of non-differentiable 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.
6.1 Differentiability, the Tangent Line-Linear 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
6.6 The Gradient and Directional Derivatives
6.7 Philosophic Implications