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<h1 style=“margin-top:1; margin-bottom:1;”>Calculus Chapter 2</h1>

<ul> <li><a href=“http://www2.math.binghamton.edu/p/calculus/resources/calculus_videos”>Home</a></li> <li><a href=“http://www2.math.binghamton.edu/p/calculus/resources/calculus_videos/chapter1”>Chapter 1</a></li> <li><a href=“http://www2.math.binghamton.edu/p/calculus/resources/calculus_videos/chapter3”>Chapter 3</a></li> <li><a href=“http://www2.math.binghamton.edu/p/calculus/resources/calculus_videos/chapter4”>Chapter 4</a></li> <li><a href=“http://www2.math.binghamton.edu/p/calculus/resources/calculus_videos/chapter5”>Chapter 5</a></li> </ul>

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===== The Derivative as a Function =====
Section 2.2 in Stewart's Calculus.

Classroom Slides PDF


===== Differentiation Formulas =====

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Section 2.3 in Stewart's Calculus.

Preclass Learning Objectives:

  • Derivative formulas for powers and roots.
  • Derivative formulas for sums/differences/products/quotients.

Classroom Slides PDF


===== Trigonometric Derivatives =====

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Section 2.4 in Stewart's Calculus.

Preclass Learning Objectives:

  • Familiarity with the limit of sin(x)/x as x approaches zero.

Classroom Slides PDF


===== The Chain Rule =====

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Section 2.5 in Stewart's Calculus.

Preclass Learning Objectives:

  • Composition and rates of change.
  • Chain Rule Formula.

Classroom Slides PDF


===== Implicit Differentiation =====

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Section 2.6 in Stewart's Calculus.

Preclass Learning Objectives:

  • An equation implicitly defines many functions.
  • Implicitly versus explicitly defined functions.
  • Basics of Implicit Differentiation.

Classroom Slides PDF


===== Rates of Change in the Sciences =====

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Section 2.7 in Stewart's Calculus.

Preclass Learning Objectives:

  • Instantaneous Rates of Change are everywhere!

Classroom Slides PDF


===== Related Rates =====

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Section 2.8 in Stewart's Calculus.

Preclass Learning Objectives:

  • Rates of change can be found by implicitly differentiating an equation. This technique is useful in obtaining information in natural, less mathematical, settings.

Classroom Slides PDF


===== Linearization and Differentials =====

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Section 2.9 in Stewart's Calculus.

Preclass Learning Objectives:

  • Lines are functions, even tangent lines.
  • Linearization of a function f(x) approximates the values of f(x).
  • The change along the y-axis can be approximated with linearization.

Classroom Slides PDF


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