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Or # 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)

Table of Content
 1 How to do Partial Derivatives of Function? 2 Second Order Partial Derivatives: 3 Chain Rule Partial Derivatives: 4 What is the chain rule in differential equations? 5 Why is the second-order partial derivative test effective?
Available on App

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:

Input:

• 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

Output:

• Partial derivative of a function with step by step calculations

## Reference:

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.