Partial Derivative Calculator | Ordinary/Partial Derivatives

Use our free online partial derivative calculator to compute ordinary derivatives of any order of one-variable functions and partial derivatives of multi-variable functions with respect to any of its independent variables.

About the Partial Derivative Calculator

This partial derivative calculator is for real-valued functions with one or more independent variables.

This mathematical tool calculates the derivatives of a function with respect to any of its independent variables, treating the remaining ones as constant if there are multiple variables.

  • If a function has only one independent variable, its derivatives are called ordinary derivatives (with respect to that variable).
  • If a function has multiple independent variables, its derivatives are called partial derivatives with respect to that specified variable.

Instructions for Using Partial Derivative Calculator

Using this ordinary and partial derivative calculator is simple:

  • Type in a real-valued function F with any number of arbitrary variables (e.g., F(x,y,z) = xyz), and also a variable in the boxes provided and press the Calculate Derivative button.
  • The derivative (such as F'(x)) or the partial derivative (such as ∂F/∂x) of the function with respect to the specified variable will be displayed in a newly added panel.
    • You can also calculate the ordinary or mixed partial derivatives of second and higher orders of the derived functions or of their primitives with respect to any variable by proceeding as above on the relevant panel.

You can close any panel by pressing × on that panel.

The calculator displays the computed derivative (ordinary or partial) in a format that allows you to trace the steps of the differentiation, reflecting the applied rules of differentiation.

Note: The notation, for example, Fxy, represents the second order partial derivative of F with respect to x, and then with respect to y. It's also denoted by ∂2F/∂y∂x.

For a single variable function, Fx represents dF/dx or F'(x), and Fxx represents F"(x) or d2F/dx2.

Calculate and graph derivatives? Try our Graphing Calculator.

F =
with respect to
 

Calculate and graph derivatives? Try our Graphing Calculator.

Tips - as you type:

  • pi is replaced by π.
  • ..t is replaced by θ.

Real-Valued Functions: Ordinary derivatives vs Partial Derivatives

The key difference lies in the number of independent variables: an ordinary derivative or just the derivative is calculated for a single-variable function, while a partial derivative is calculated for a multivariable function with respect to any of its independent variables. Note that when calculating partial derivatives, you treat all other variables as constants.

An example of an ordinary derivative is merely the derivative of the function f(x) = x^2, which is f'(x) = 2x. An example of a partial derivative is the partial derivative of the function g(x,y) = xy with respect to x, which is ∂g/∂x = y (treating y as a constant).

Since a partial derivative calculator can handle functions with any number of variables, it is inherently an ordinary derivative calculator or simply a derivative calculator for one-variable functions as well. This means it can calculate derivatives of single-variable functions like f(x) with respect to its only variable x, namely f'(x).