Partial Derivative Calculator: Ordinary & Partials

Explore our user-friendly and versatile ordinary & partial derivative calculator. With this tool, you can calculate symbolic ordinary derivatives (such as f'(x), df/dx, dy/dx, or f''(x)) of single-variable functions. Also calculate partial derivatives (such as ∂f/∂x or 2f/∂y∂x) of any order for functions with any number of variables.

To use this Partial Derivative Calculator:

  1. Enter a function F (e.g., xyz) that you want to differentiate.
  2. Specify the variable you want to differentiate with respect to.
  3. Press the Calculate Derivative button.

The multivariable derivative calculator will then display the calculated derivative (ordinary or partial) in a new panel. The format will allow you to trace the steps of the differentiation, reflecting the applied rules of differentiation.

Note: The notation, for example, Fxy, represents the partial derivative of F with respect to x, followed by 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.

  • A useful feature of this derivative calculator is that you can also calculate higher-order ordinary or partial derivatives. Simply follow the same steps described above on the corresponding panel.

To close a panel, simply press the × button.

What is the difference between ordinary and partial derivatives? The key difference lies in the number of independent variables: an ordinary 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 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 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).

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