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derivative Calculator

Partial Derivative Calculator

Enter the function, select variable, and mention differentiation order. The tool will differentiate the function multi times up to the order you entered, with steps shown.

Enter a function f(x,y): Hint: Please write e^x as e^{x}


Derivative W.R.T ?

How many times? (Differentiate)

Available on App

Download Partial Derivatives Calculator App for Your Mobile, So you can calculate your values in your hand.


An online Partial derivative calculator is used to differentiate mathematical functions that contain multiple variables. Yes, this multivariable derivative calculator can differentiate a certain function multiple times.

What Is a Partial Derivative?

The partial derivative is defined as the derivative of a multivariable function with respect to one variable, while all other variables remain unchanged.

When a function has two variables x and y that are independent of each other, then what to do there! Simply,

  • If you require differentiating the function with respect to “x”, then you should keep the variable “y” constant and differentiate.
  • On the other hand, if you need to differentiate the function with respect to “y”, then make the variable “x” constant. The symbol “∂” is generally used to indicate chain rule partial derivatives

How to do a Partial Derivative of Function?

You can do these derivation calculations of a function manually by stick to these steps:

Take a function to compute the partial derivative
The derivative of a constant is zero
When applying a derivative to a variable, only the derivative of that particular variable is solved
Solve all the functions for getting the results

Second Partial Derivatives:

The high-order derivative is very important for testing the concavity of the function and confirming whether the endpoint of the function is maximum or minimum. Since the function f (x, y) is continuously differentiable in the open region, you can obtain the following set of partial second-order derivatives:

  • F_{xx} = ∂fx / ∂x, where function f (x) is the first partial derivative of x.
  • F_{yy} = ∂fy / ∂y, where function f (y) is the first order derivative with respect to y.

How Does Partial Derivative Calculator Work?

Our multivariable derivative calculator differentiates the given functions by following these steps:


  • First, enter a function for differentiation
  • Now, select the variable for derivative from the drop-down list
  • Then, select how many times you need to differentiate the given function
  • Hit the calculate button


  • Partial derivative of a function with step by step calculations


From the source of Wikipedia: Surface in Euclidean space, abuse of notation, Clairaut’s theorem, Optimization, Thermodynamics, quantum mechanics and mathematical physics.

From the source of Brilliant: instantaneous rate of change or slope, single-variable differentiation, Linearity, Product Rule, Chain Rule, Vector Calculus and Higher-order Derivatives, mixed derivative.

From the source of Khan Academy: multivariable function, three-dimensional graphs, single variable calculus, two-dimensional inputs, pre-evaluating.