Explore our userfriendly and versatile Partial Derivative Calculator. With this tool, you can calculate partial derivatives (such as ∂f/∂x
or ∂^{2}f/∂y∂x
) of any order for functions with any number of variables. Also calculate symbolic ordinary derivatives (such as f'(x)
, df/dx
or dy/dx
) of singlevariable functions .
To use this Partial Derivative Calculator:

Enter a function
F
(e.g.,xyz
) that you want to differentiate.  Specify the variable you want to differentiate with respect to.
 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, F_{xy}
, represents the partial derivative of F
with respect to x
, followed by y
. It's also denonted by ∂^{2}F/∂y∂x
.
For a single variable function, F_{x}
represents dF/dx
or F'(x)
, and F_{xx}
represents F"(x)
or d^{2}F/dx^{2}
.
 A useful feature of this derivative calculator is that you can also calculate higherorder 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 singlevariable 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 singlevariable functions like f(x)
with respect to its only variable x
, namely f'(x)
.