# Activities

• • • ##### Subject Area

• Math: Calculus: Derivatives

• ##### Author 9-12

45 Minutes

• ##### Device
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™
• TI-Nspire™ CAS
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

3.2

• ##### Report an Issue

Implicit Differentiation

#### Activity Overview

Students find the derivative of a relation, F(x,y), that is not solved for y.

#### Key Steps

• Students will be introduced to the concept of implicit differentiation. Students will begin by solving the equation of a circle for y and then find the derivative of the relation using already familiar methods.

• Next, students will use the impDif command to find an alternate form of the derivative, and verify that the two forms are equal.

• Students will learn how to perform implicit differentiation by hand, using the impDif command to check their results. Then students will be asked to find the numerical derivative of a relation for specific x-values. A graphical connection to the results found using implicit differentiation will then be made.