Implicit Derivative Calculator

How to Use the Implicit Derivative Calculator

This guide will walk you through the process of using the Implicit Derivative Calculator to find the derivative of an implicit equation at a given point, as well as additional related information like the slope and angle with the x-axis.

Step 1: Select the Equation Type

Begin by selecting the type of equation you wish to analyze. The calculator offers the following options:

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

Make sure to select the appropriate option based on the kind of curve involved in your problem.

Step 2: Provide the Point of Interest

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

• x-coordinate: Enter the value for x. This field is mandatory and requires a numerical value.
• y-coordinate: Enter the value for y. Similar to the x-coordinate, this field is also necessary and expects a number.

Ensure that both coordinates correspond to a point on the selected curve.

Step 3: Enter Additional Parameters

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

• Circle: Enter the radius (r). This is applicable only for the Circle option.
• Ellipse/Hyperbola: Provide values for a and b, where these represent the semi-major and semi-minor axes respectively.

Please note that while these fields are not flagged as required within the calculator, omitting them for applicable equations will result in incorrect calculations.

Step 4: Review the Calculated Results

Once all required and applicable fields are filled out correctly, the calculator will process your input and display the following results:

• dy/dx at point (x,y): This is the implicit derivative of the equation at the specified point.
• Slope: This represents the inclination of the tangent to the curve at the specified point.
• Perpendicular Slope: This signifies the slope of a line perpendicular to the tangent at the same point.
• Angle with x-axis (degrees): Calculated as the angle between the tangent at the selected point and the x-axis, given in degrees.

The results will be displayed with the specified degrees of precision, ensuring clarity and correctness in your analysis.

Conclusion

Using this Implicit Derivative Calculator, you can effortlessly compute derivatives and related metrics for common implicit equations. Ensure that all inputs are correct and applicable to achieve precise results.