Partial Derivative Calculator

How to Use the Partial Derivative Calculator

This guide will help you understand how to use the Partial Derivative Calculator effectively to find partial derivatives of functions and evaluate them at specific points. Additionally, you’ll learn how to find the gradient magnitude for a given function. Follow the steps below to get started.

Step 1: Select a Function

Begin by selecting the function for which you want to find the partial derivative. You can choose from the following options:

• f(x,y) = x² + y²
• f(x,y) = x²y
• f(x,y) = sin(x)cos(y)
• f(x,y) = e^(x+y)
• f(x,y) = ln(xy)

This step is necessary, and you must select a function to proceed.

Step 2: Enter Values for x and y

In the respective fields, input the values for x and y at which you would like to evaluate the partial derivative. These values should be numerical and can include decimal points with a step of 0.1 to ensure precision in calculations. Both values are required.

Step 3: Select the Variable for Differentiation

Determine the variable with respect to which you wish to differentiate the function. You can choose either:

• x
• y

This selection is crucial as it directs the calculator to compute the appropriate partial derivative.

Step 4: Review the Results

Upon entering all necessary inputs, the calculator will provide the following results:

• Partial Derivative: This field displays the calculated derivative of the selected function with respect to the chosen variable.
• Evaluated at Point: Here, you will see the value of the partial derivative evaluated at the specified values for x and y. The result is provided up to four decimal places for accuracy.
• Gradient Magnitude: This result gives you the magnitude of the gradient vector of the function, calculated at the provided x and y values. The magnitude is computed using the partial derivatives with respect to both x and y, ensuring a comprehensive understanding of the function’s slope at the given point.

By following these steps, you’ll effectively utilize the Partial Derivative Calculator to analyze functions, derive insights from their behavior at specific points, and investigate their gradient magnitudes.