Implicit Differentiation Calculator

How to Use the Implicit Differentiation Calculator

Using the Implicit Differentiation Calculator is a straightforward process that involves a few simple steps. This guide will walk you through each step to ensure you correctly input your data and interpret the results provided by the calculator.

Step 1: Select the Equation Type

The first step in using the calculator is to select the type of equation you want to work with. The calculator supports three types of equations:

• Circle Equation: (x² + y² = r²)
• Ellipse Equation: (x²/a² + y²/b² = 1)
• Hyperbola Equation: (x²/a² – y²/b² = 1)

Select the appropriate equation type from the provided dropdown menu.

Step 2: Enter the Coordinates

Next, you need to enter the coordinates of the point at which you want to find the derivative:

• x-coordinate: Input the x-value of the point. Ensure that you enter a numerical value, as this field is required and supports steps of 0.1.
• y-coordinate: Input the y-value of the point. Like the x-coordinate, this field is required and supports steps of 0.1.

Step 3: Provide Additional Parameters

Depending on the type of equation selected, you may need to provide additional parameters:

• Radius (r) for Circle: If you’ve selected the Circle equation, enter the radius. This field is optional but should be a non-negative number if used.
• a-value for Ellipse/Hyperbola: If you’ve selected Ellipse or Hyperbola, enter the ‘a’ value. This should be a non-negative number.
• b-value for Ellipse/Hyperbola: Also for Ellipse or Hyperbola, provide the ‘b’ value, which should be non-negative.

Step 4: Calculate and Interpret the Results

Once all required fields are filled out, the calculator will automatically compute several results:

• dy/dx at Given Point: This is the derivative at your provided point, calculated using implicit differentiation.
• Slope: The slope of the tangent line at the given point, which is essentially the same as the derivative.
• Normal Slope: The slope of the line normal (perpendicular) to the tangent line at the given point.
• Angle with x-axis (Radians): The angle that the tangent line makes with the x-axis, presented in radians.
• Angle with x-axis (Degrees): The aforementioned angle, converted to degrees.

Review these results carefully to gain insights into the behavior of the curve at the specified point. The values are formatted for precision to assist with accurate interpretations.

By following these steps, you can efficiently use the Implicit Differentiation Calculator to perform necessary calculations and analyze the results.