About the Derivative Calculator (Ordinary & Partial)
Our versatile ordinary & partial derivative calculator allows you to calculate symbolic ordinary derivatives, such as f'(x) of single-variable functions. You can also calculate partial derivatives, such as Fx (also denoted as ∂f/∂x) for real-valued functions with any number of variables.
Guide to Use our Derivative Calculator
It's easy to use this ordinary and partial derivative calculator:
- Type in a function F with any number of arbitrary variables (e.g., xyz).
- Type in a variable you want to differentiate the function with respect to.
- Press the Calculate Derivative button.
The multivariable derivative calculator displays the calculated derivative (ordinary or partial) in a newly added panel. The derivative is presented in a format that allows you to trace the steps of differentiation, reflecting the applied rules of differentiation such as the chain rule.
Furthermore, you can then calculate the ordinary or partial derivatives of the second-order (and consequently, higher-order) of the derived functions with respect to any variable by typing a variable on the relevant panel and pressing Calculate Derivative.
You can close any panel by pressing ×.
Ordinary Derivatives vs Partial Derivatives
The key difference lies in the number of independent 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 a specified variable. Note that when calculating partial derivatives, the partial differentiation calculator treats 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).
Interested in calculating derivatives and easily graphing 1st and 2nd order derivatives? Try our Graphing Calculator.