Derivatives: Flipped Calculus at Binghamton SUNY [Department of Mathematics and Statistics, Binghamton University]

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<h1 style=“margin-top:1; margin-bottom:1;”>Flipped Calculus 1 at Binghamton</h1>

<ul> <li><a href=“http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources”>Home</a></li> <li><a href=“http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/limits”>Limits</a></li> <li><a href=“http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/derivatives”>Derivatives</a></li> <li><a href=“http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications”>Applications</a></li> <li><a href=“http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/integrals”>Integrals</a></li> </ul>

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

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===== 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.

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===== 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.

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===== 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.

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===== 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 Differntiation.

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===== 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!

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===== 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.

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<h1>Laura Anderson and Joseph Brennan</h1>

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