Directional Derivative Calculator

How to Use the Directional Derivative Calculator

This guide will walk you through the steps required to determine the directional derivative of a function using the Directional Derivative Calculator. Follow each step carefully to ensure accurate results.

Step 1: Selecting the Function

• Select a function from the dropdown list labeled “Select Function f(x,y)”. The options include:
  • f(x,y) = x² + y²
  • f(x,y) = x² – y²
  • f(x,y) = xy
  • f(x,y) = sin(x)cos(y)

Step 2: Input the Point and Direction

• Enter the x-coordinate (a) of the point at which you want to compute the derivative in the “Point x-coordinate (a)” field. This should be a number and the field is required.
• Enter the y-coordinate (b) of the point in the “Point y-coordinate (b)” field. This is also a required field.
• Provide the x-component of the direction vector in the field labeled “Direction Vector x-component”.
• Provide the y-component of the direction vector in the field labeled “Direction Vector y-component”.
• Ensure all numerical entries are to the desired precision with a step value of 0.1.

Step 3: Calculating the Derivatives and Directional Derivative

• Once all inputs are provided, the calculator will automatically compute the following results:
  • ∂f/∂x at point (a,b): This gives the rate of change of the function f(x,y) with respect to x at the specified point. It is displayed with four decimal places of precision.
  • ∂f/∂y at point (a,b): This calculates the rate of change of the function with respect to y, also precise to four decimal places.
  • Direction Vector Magnitude: The magnitude of your specified direction vector is calculated, allowing you to understand the scale of your direction vector.
  • Directional Derivative: This value is calculated by combining the partial derivatives with the components of your direction vector, normalized by the magnitude of the direction vector. It represents the rate of change of the function in the specified direction.

By following these steps, you can effectively use the Directional Derivative Calculator to explore how a function changes in a particular direction from a given point.