Education Technology

Differentiation

Published on 06/09/2008

Activity Overview

In this activity, students explore estimated and exact results for derivatives, tangent lines, implicit differentiation, and symbolic differentiation.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 15 - 26 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:
    Finding Slope and the Tangent Line:

  • Enter the function and find average rate of change with an arbitrary increment
  • Find the numerical derivative and graph to find the tangent line

  • Find the numerical derivative and graph the function
  • Compute a point on the graph and estimate the value of the derivative
  • Plot the tangent line


  • Exact Derivatives:
  • Explore derivatives with limits and built-in derivative command


  • Implicit Differentiation:
  • Use implicit theorem to compute the derivative in terms of x and y
  • Evaluate the derivative for different values of x and y
  • Compute the derivative directly by writing y as a function of x


  • Solve for the Function y(x):
  • Find values of y that give the function a value of zero and differentiate
  • Evaluate the derivative for a particular value of x
  • Graph the function and draw tangent lines


  • Symbolic Differentiation:
  • Use the differentiate command with undefined functions
  • After the Activity

    Students will complete the practice exercise problems.

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary