1 / 14

Understanding Derivatives: Rates of Change and Applications in Calculus

Explore the concept of derivatives and how they represent the rate of change in various contexts, including the circumference of a circle, area of a square, and volume of a cylinder. Learn about different notations (Newton, L'Hôpital, Leibniz) and algebraic rules applicable to constant and power functions. Understand how to find instantaneous rates of change and derivatives through clear examples, including a practical problem involving a cylindrical tank filling with water. Perfect for high school and college students looking to grasp essential calculus principles.

dawn
Télécharger la présentation

Understanding Derivatives: Rates of Change and Applications in Calculus

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 1008 : The Shortcut AP CALCULUS

  2. Notation: The Derivative is notated by: Newton L’Hopital Leibniz

  3. Notation: Find the rate of change of the Circumference of a Circle with respect to its Radius. Find the rate of change of the Area of a Square with respect to the length of a Side. Find the rate of change of the Volume of a Cylinder with respect to its Height.

  4. Algebraic Rules A). A Constant Function REM:

  5. Algebraic Rules B). A Power Function Rewrite in exponent form!

  6. Algebraic Rules C). A Constant Multiplier

  7. Algebraic Rules D). A Polynomial REM:

  8. Example: Positive Integer Powers, Multiples, Sums, and Differences Calculator: [F3] 1: d( differentiate or [2nd ] [ 8 ] d( d(expression,variable) d( x^4 + 2x^2 - (3/4)x - 19 , x )

  9. Do it all !

  10. A cylindrical tank with radius 4 ft is being filled with water. Write the equation for the volume of the cylinder. Find the instantaneous rate of change equation of the volume with respect to the height. Find the instantaneous rate of change in Volume when the height is 9 ft.

  11. Second and Higher Order Derivatives

  12. Second and Higher Order Derivatives

  13. Example: Find all the derivatives.

  14. Last Update • 08/12/10

More Related