Partial Derivatives

A which maps can be differentiated in two ways

1. Treat y as a constant and differentiate with respect to x, denoted as
2. Treat x as a constant and differentiate with respect to y, denoted as

Derivatives of & are called the first partial derivatives of f

Notation for partial derivatives:

• subscript notation
• operator notation

Definition: The partial derivative of f at point (a, b) are defined as:

Higher Derivatives - We can also compute higher derivatives for f(x, y) such as

Second derivatives of

this will always hold true if both of them are continuous