Download presentation

Presentation is loading. Please wait.

Published byGloria Devin Modified over 2 years ago

1
2.3 Rules for Differentiation Colorado National Monument Vista High, AB Calculus. Book Larson, V9 2010Photo by Vickie Kelly, 2003

2
If the derivative of a function is its slope, then for a constant function, the derivative must be zero. example: The derivative of a constant is zero.

3
If we find derivatives with the difference quotient: (Pascal’s Triangle) We observe a pattern: …

4
examples: power rule We observe a pattern:…

5
examples: constant multiple rule: When we used the difference quotient, we observed that since the limit had no effect on a constant coefficient, that the constant could be factored to the outside.

6
(Each term is treated separately) constant multiple rule: sum and difference rules:

7
Example: Find the horizontal tangents of: Horizontal tangents occur when slope = zero. Plugging the x values into the original equation, we get: (The function is even, so we only get two horizontal tangents.)

13
First derivative (slope) is zero at:

14
product rule: Notice that this is not just the product of two derivatives. This is sometimes memorized as:

15
quotient rule: or

16
Higher Order Derivatives: is the first derivative of y with respect to x. is the second derivative. (y double prime) is the third derivative.is the fourth derivative. We will learn later what these higher order derivatives are used for.

Similar presentations

OK

Section 3.3a. The Do Now Find the derivative of Does this make sense graphically???

Section 3.3a. The Do Now Find the derivative of Does this make sense graphically???

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on javascript events tutorial Ppt on event driven programming c# Ppt on boilers operations manager Ppt on field study 2 Ppt on social problem in contemporary india Ppt on teamviewer 9 Ppt on high voltage engineering ppt Hrm ppt on recruitment process Parathyroid gland anatomy and physiology ppt on cells Ppt on different model of atoms