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calculus:resources:calculus_videos:chapter2

## 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!

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.