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calculus:resources:calculus_videos:chapter2
Calculus Chapter 2
The Derivative as a Function
Section 2.2 in Stewart's Calculus.
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.
Trigonometric Derivatives
Section 2.4 in Stewart's Calculus.
Preclass Learning Objectives:
- Familiarity with the limit of sin(x)/x as x approaches zero.
The Chain Rule
Section 2.5 in Stewart's Calculus.
Preclass Learning Objectives:
- Composition and rates of change.
- Chain Rule Formula.
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.
Rates of Change in the Sciences
Section 2.7 in Stewart's Calculus.
Preclass Learning Objectives:
- Instantaneous Rates of Change are everywhere!
Related Rates
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.
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.
calculus/resources/calculus_videos/chapter2.txt · Last modified: 2015/11/21 16:35 by kaz