“The Tangent Line of an Implicit Relation”
The Tangent Line of an Implicit Relation
Jul 2, 2004
- This site is a member of a large collection of WebMathematica scripts written by the author. The rather simple but useful applet allows the user to compute the derivative implicitly of a user defined expression involving most of the commonly used functions from calculus. The applet gives one intermediate step and a (Mathematica) simplified expression for the derivative.
- Type of Material:
- Recommended Uses:
- Study aid for calculus students.
- Technical Requirements:
- It requires a "Java-enabled" browser.
- Identify Major Learning Goals:
- To help the student better understand implicit differentiation.
- Target Student Population:
- Calculus students.
- Prerequisite Knowledge or Skills:
- Knowledge of the derivative including product, quotient, and chain rules
- Implicit differentiation can be challenging for many students in a first course in Calculus. This applet will allow the user to work several examples giving them the first step and a simplified expression for y?.
The user can input expressions (using Mathematica syntax) involving many of commonly used functions as well as general expressions involving powers of both x and y.
- A little more explanation should be given of the fact that in the equation relating y and x, y is a function of an independent variable x, and dy/dx is to be found.
- This applet will allow students to check their work on the even numbered problems when solutions are not supplied by their text book.
Because the user has the flexibility to choose the functions, it is easy to choose several very meaningful examples.
- The use of this applet is rather limited to quick check of implicit differentiation problems. It is, however, just one of the ?tools? in the large collection of the parent site.
- The applet has only one button and one window used for inputting expressions to be differentiated. It is so intuitive that no instructions are necessary. The only possible difficulty may be due to the fact that it uses Mathematica function syntax which is slightly different from that used by most of graphing calculators. The average user can begin using the applet immediately.
- This applet should have a link to the page explaining Mathematica syntax found at:
- Creative Commons: