This tool calculates the partial derivative of a given multivariable function with respect to one of its variables.

## How to Use the Partial Derivative Calculator

To use this calculator, enter a multivariable function in terms of x, y, and z in the input field provided. Select the variable with respect to which you want to take the partial derivative from the dropdown menu. Click “Calculate” to see the result. The calculator will compute the partial derivative of the given function with respect to the specified variable using numerical differentiation.

### Example

For the function `3*x*y + 2*y*z - z*x^2`

, if you want to find the partial derivative with respect
to x, you would enter “3*x*y + 2*y*z – z*x^2” in the function input field, select “x” from the dropdown,
and click “Calculate”. The result will be displayed in the result field.

### Limitations

Please note that this calculator uses numerical differentiation, which means it approximates the derivative using finite differences. This method can introduce small numerical errors, especially for functions with rapid changes. The default evaluation point is (x=1, y=1, z=1). For more precise calculations, it is recommended to verify the results using symbolic differentiation when possible.

## Use Cases for This Calculator

### Calculate Partial Derivative with Respect to x

Enter a multivariable function, and with a click, find the partial derivative with respect to x. This calculator allows you to easily differentiate functions with respect to x without the hassle of manual calculations.

### Compute Partial Derivative with Respect to y

Input your function, and obtain the partial derivative with respect to y effortlessly. No need to spend time on tedious differentiation – let the calculator do the work for you and get accurate results within seconds.

### Derive Partial Derivative with Respect to z

Simply type in your function, and receive the partial derivative with respect to z promptly. Whether it’s a simple or complex function, this calculator ensures you get the correct derivative without any errors.

### Find Second Partial Derivative with Respect to x and y

Use this calculator to determine the second partial derivative by entering your function and selecting the variables x and y. Quickly obtain the second derivative without any confusion or mistakes.

### Calculate Second Partial Derivative with Respect to y and z

Enter your function, choose the variables y and z, and get the second partial derivative instantly. Ensure accuracy in your calculations and save time with this efficient calculator.

### Derive Second Partial Derivative with Respect to x and z

Input your function and select x and z as variables to compute the second partial derivative. With just a click, you’ll have the correct second derivative, making your math tasks simpler and error-free.

### Calculate Third Partial Derivative with Respect to x, y, and z

Easily find the third partial derivative by entering your function and selecting x, y, and z as variables. This calculator streamlines the process, allowing you to focus on your analysis rather than manual computations.

### Check Mixed Partial Derivatives (xy, xz, yz)

Check for mixed partial derivatives such as xy, xz, and yz by inputting your function. Quickly verify the mixed derivatives to ensure the accuracy of your mathematical analysis, saving you time and effort.

### Handle Logarithmic and Trigonometric Functions

This calculator handles logarithmic and trigonometric functions seamlessly. Input functions involving logarithms or trigonometric functions like sine and cosine, and effortlessly compute partial derivatives without worrying about complex calculations.

### Access Results with Clear Step-by-Step Solutions

Receive not just the final answer but also step-by-step solutions to understand how the partial derivatives were calculated. Clear explanations help you grasp the concept better and enhance your learning experience with this calculator.