Higher Order Derivatives

This calculus video tutorial provides a basic introduction into higher order derivatives. it explains how to find the second derivative of a function.

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Derivatives - Fast Review:

Equation of the Tangent Line:

Derivatives - Horizontal Tangent Line:

The Equation of The Normal Line:

The Equation of The Secant Line:

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Average and Instantaneous Velocity:

Instantaneous Rate of Change:

Derivatives of Rational Functions:

Derivatives of Radical Functions:

Derivatives of Fractions:

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Derivatives - Higher Order:

Simplifying Derivatives:

Derivatives - The Product Rule:

Derivatives - The Quotient Rule:

Derivatives - The Chain Rule:

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Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

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[charleshudson]

In Kinematics, the Third, Fourth, Fifth and Sixth derivatives have names. They are (seriously): Jerk, Jounce (also called Snap), Crackle and Pop. They are used by mechanical engineers in the design of cam shafts, railroad track curves, pistons, etc. Acceleration is never really instantaneous. Jerk is the time rate of change of acceleration, that is, the small change in inertia when a constant force is initially applied. Jerk is the time rate of change of Jounce. When you are riding in a car under 'constant' acceleration but over a rough surface, the acceleration is not really constant, but rapidly changing, producing Jerk. To get the smoothest ride on a roller coaster, or on a railroad curve, an engineer considers the Jerk and the Jounce. (Or Snap.) As for Crackle and Pop, they are less used, (if at all), but expressions of the reality that much of applied physics is idealized mechanics. I'm answering my own question, posed below:

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[georgesadler]

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I'll be having a long quiz on derivatives in the next 6 hours and this really helped

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