The Derivative as a Function


Section 2.2 in Stewart's Calculus.

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Differentiation Formulas

Section 2.3 in Stewart's Calculus.

Preclass Learning Objectives:

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

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Trigonometric Derivatives

Section 2.4 in Stewart's Calculus.

Preclass Learning Objectives:

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

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The Chain Rule

Section 2.5 in Stewart's Calculus.

Preclass Learning Objectives:

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

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Implicit Differentiation


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.

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Rates of Change in the Sciences

Section 2.7 in Stewart's Calculus.

Preclass Learning Objectives:

  • Instantaneous Rates of Change are everywhere!

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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.

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Linearization and Differentials


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.

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