A partial derivative is an operation on a multivariable function which describes the rate of change of the function with respect to a certain variable.

Notation

Partial derivatives can be written similarly to derivatives but with the 's being replaced by the symbol.

For example the partial derivative of with respect to could be written as either

or

Definition

With an variable function

Where represents the variable with which the partial derivative is being taken with respect to

For example with a 3 variable function this equation would take the form when differentiating with respect to (the first variable or )

Calculating

Partial derivatives can be calculated the same way as normal derivatives by treating the variable the partial derivative is taken with respect to as the variable and the rest as constants.

For example