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Alignment
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Subject Area
- Math: Calculus: Applications of the Derivative
Author

Texas Instruments
Level

9-12
Activity Time

45 Minutes
Device
- TI-Nspire™ Navigator™
- TI-Nspire™ CAS
Software

TI-Nspire™ CAS
TI-Nspire Version

3.0
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Exponentially Fast Derivative

Activity Overview

In this activity, students will investigate the derivative of exponential functions. For e^x, students will explore the slope of the tangent graphically and use CAS functionality to discover the chain rule for exponential functions. Similarly, a^x is explored graphically and CAS functionality is used to discover the rule.

Key Steps

Part 1 begins with foundational questions that often need reviewed. Graphical reinforcement and self-check multiple-choice questions strength students’ understanding and retention.
Students will realize that the derivative of e^x is unlike the derivative of a polynomial or the power function xⁿ. Students use CAS functionality to discover the rule for the derivative of e^u^(x).
Observations of an exponential function and its derivative are made. Inquiry questions are provided for the teacher to draw out deeper understanding. Students will algebraically and numerically confirm observations. Problems are provided to develop proficiency with the Chain Rule as it applies to exponential functions.

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Exponentially Fast Derivative

Activity Overview

Key Steps

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