Part 1 Differential Calculus

Definition and Basics

The differential calculus (or differentiation) is an essential part of analysis and therefore a field of mathematics. The central topic of differential calculus is the calculation of local changes of functions.

While a continuous function continuously assigns certain output values to its input values, differential calculus determines how strongly the output values change in response to very small changes in the input values. It is closely related to integral calculus, with which it is collectively referred to as infinitesimal calculus.

The derivative of a function is used to represent local changes in a function and is at the same time a fundamental concept of differential calculus. Instead of derivative, the term diff

erential quotient is also used; its geometric interpretation is the slope of the tangent line.

Part 2 Differentiation Rules

Part 3 Graphical Differentiation

Part 4 Partial Differentiation