Learning how to use derivativesBy: Dylan Brown

Textbook Definition Type of Limit Slope of a tangent Velocity/Rate of

change

Source: Stewart, James. "Chapter 2." Essential Calculus. Belmont, CA: Thomson Brooks/Cole, 2007. 73. Print

Photo Source: Ptwo. 122. 2009. Photograph. Flickr. (URL: http://www.flickr.com/photos/ptwo/3164159940/)

Where did derivatives come from?

Calculus has been around for centuries

Newton and Leibniz “invented” calculus

Newton’s laws of physics explained rate of change

Source: Schechter, Eric. "Why Do We Study Calculus? Or, a Brief Look at Some of the History of Mathematics." Thesis. Vanderbilt University, 2006. Why Do We Study Calculus? 23 Aug. 2006. Web. 27 Feb. 2012.

Photo Source: Lednichenko, Olga. Newton-ISSAC-olga, Olga Shulman Lednichenko, Lednichenko, Lednichenko-olga, Olgalednichenko, Lednichenko-olya, Olya Lednichenko, IMGAES AND PHOTOS OLGA LEDNICHENKO - Copy. 2011. Photograph. Flickr.

What are they used for?

Slope of a tangent Can be used at any point

Helpful in physics Applied to many areas of calculus

Rate of Change

Why do I have to learn about it?

Can be very helpful in physics Huge part of calculus

Many professions require Calculus I

Definition of Derivative At a point P(a,f(a))

m=

Determines slope at point P

Derivative Rules Power rule: Constant Multiple: Product Rule:

Starting with the basics Power and Constant Rule:

Find derivative or

Can be solved with either Power+Constant or just Power Rule

Product Rule

Uses power rule and product rule

Physics Newton discovered calculus and made

his law of physics Derivatives solve physics problems

Position: Velocity: Acceleration:

Example If a car’s position can be determined

with the equation then what equation would determine the car’s velocity or acceleration at any given point?

Velocity: Acceleration:

Visual ExampleAt any point, I can figure what the position, velocity, or acceleration is of the car. For instance, for the position and , then for time x=2 seconds, the position would be 32 meters and the velocity at the instant x=2 would be 48 meters/second2

Conclusion of Derivatives

Fundamental to calculus Fundamental to physics

Physicists “invented” calculus Several rules make it easier

There is much more to calculus than what I have showed you

Text Sources Stewart, James. "Chapter 2." Essential Calculus. Belmont, CA:

Thomson Brooks/Cole, 2007. 73. Print Schechter, Eric. "Why Do We Study Calculus? Or, a Brief Look at

Some of the History of Mathematics." Thesis. Vanderbilt University, 2006. Why Do We Study Calculus? 23 Aug. 2006. Web. 27 Feb. 2012. <http://www.math.vanderbilt.edu/~schectex/courses/whystudy.html>.

Photo Sources SLIDE 2: Ptwo. 122. 2009. Photograph. Flickr. (URL:

http://www.flickr.com/photos/ptwo/3164159940/) SLIDE 3: Lednichenko, Olga. Newton-ISSAC-olga,

Olga Shulman Lednichenko, Lednichenko, Lednichenko-olga, Olgalednichenko, Lednichenko-olya, Olya Lednichenko, IMGAES AND PHOTOS OLGA LEDNICHENKO - Copy. 2011. Photograph. Flickr. (URL: http://www.flickr.com/photos/olga-lednichenko-photos-albums-images/6417814081/)

SLIDE 13: Microsoft Clip Art

The End