Partial Derivative (Noun)
Meaning
The derivative of a function of two or more variables with respect to a single variable while the other variables are considered to be constant.
Classification
Nouns denoting cognitive processes and contents.
Examples
- The partial derivative of the function f(x, y) with respect to x is calculated by differentiating the function while treating y as a constant.
- To find the maximum or minimum of a function of two variables, the partial derivatives with respect to both variables must be set equal to zero.
- The partial derivative of the function z = f(x, y) with respect to y is often denoted as ∂z/∂y.
- In thermodynamics, the partial derivative of the internal energy with respect to the volume of the system is related to the pressure of the system.
- The partial derivative of a function of multiple variables can be used to analyze the effect of a change in one of the variables on the value of the function.