Partial Derivative

A partial derivative is a concept in multivariable calculus that deals with the rate of change of a function with respect to one variable while keeping other variables constant. Partial derivatives are applicable to functions with multiple variables, such as f(x, y) or g(x, y, z).

To calculate the partial derivative of a function with respect to a specific variable, we differentiate the function with respect to that variable while treating the other variables as constants. Notation for partial derivatives include ∂f/∂x or ∂f/∂y, where the symbol ∂ (called “del” or “partial”) indicates that we are taking a partial derivative.

Partial derivatives are essential in various applications, such as optimizing multivariable functions in economics, analyzing surface properties in physics, and understanding the behavior of functions in many other fields. Additionally, partial derivatives play a crucial role in the formulation of gradient and Jacobian matrices, which are used in optimization and transformation problems.