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Math Calculators ▶ Partial Derivative Calculator

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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.

**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

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

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.

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

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.