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Series: Calculus: Techniques for Finding the Derivative

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About this Series

  • Lessons: 8
  • Total Time: 2h 2m
  • Use: Watch Online & Download
  • Access Period: Unlimited
  • Created At: 07/29/2009
  • Last Updated At: 05/13/2011

In this 8-lesson series of lessons, Professor Burger will introduce you to the most common rules for differentiation: the power rule, the product rule, the quotient rule, and the chain rule. In addition to coming to understand each of these different techniques for finding derivatives, we'll also work with problems that require us to use multiple different techniques in order to find a function's derivative.

The power rule states that if N is a rational number, then the function f ( x) = x^N is differentiable and f ?( x) = Nx^(N?1). We'll look at how the power rule works, examine a quick proof of the general case of the power rule, and look at a few uses and extensions of the power rule. Two extensions of the power rule are the constant multiple rule and the sum rule. The constant multiple rule says that for any constant, c, the derivative of c times differentiable function f(x) is the same as f'(x) times c. The sum rule states that for two differentiable functions, f(x) and g(x), the derivative of their sum is the same as the sum of their derivatives, or f'(x) + g'(x) = [f(x) + g(x)]'

The derivative of a product or quotient of two functions is not necessarily equal to the product or quotient of the two derivatives. The product rule states that if p(x) = f(x) * g(x), where f and g are differentiable functions, then p is differentiable and p'(x) = f(x)g'(x) + g(x)f'(X). The quotient rule states that if q( x) = f ( x) / g( x) , where f and g are differentiable functions, then q is differentiable except where g( x) = 0 and q'(x) = [g(x)f'(x) - f(x)g'(x)] / [g(x)^2]

A composite function is made up of layers of functions inside of functions. Some techniques of differentiation become very cumbersome when applied to composite functions. The chain rule states that if f ( x) = g(h( x)) , where g and h are differentiable functions, then f is differentiable and f ?( x) = g?(h( x)) ? h?( x) .

Taught by Professor Edward Burger, this series comes from a comprehensive Calculus course. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/calculus. The full course covers limits, derivatives, implicit differentiation, integration or antidifferentiation, L'Hopital's Rule, functions and their inverses, improper integrals, integral calculus, differential calculus, sequences, series, differential equations, parametric equations, polar coordinates, vector calculus and a variety of other AP Calculus, College Calculus and Calculus II topics.

About this Author

Thinkwell
Thinkwell
2174 lessons
Joined:
11/13/2008

Founded in 1997, Thinkwell has succeeded in creating "next-generation" textbooks that help students learn and teachers teach. Capitalizing on the power of new technology, Thinkwell products prepare students more effectively for their coursework than any printed textbook can. Thinkwell has assembled a group of talented industry professionals who have shaped the company into the leading provider of technology-based textbooks. For more information about Thinkwell, please visit www.thinkwell.com or visit Thinkwell's Video Lesson Store at http://thinkwell.mindbites.com/.

Thinkwell lessons feature a star-studded cast of outstanding university professors: Edward Burger (Pre-Algebra through...

Lessons Included

Nopic_dkb
Ogres
04/22/2011
~ Russell7

ARE NOT LIKE ONIONS!

Nopic_orng
thank you!
02/23/2010
~ Aisha1

thank you! saved me on my midterm!!!!

Nopic_blu
A nice start to the quotient rule.
01/24/2009
~ travis5818

There are a few things I disagree with though a bit. One of which is the chanting deal. All you really need to do for product and quotient rules is memorize 2 letters and a ' symbol with them.

product rule = fg' + gf' (where you make f = to a function and g = to a function)

quotient rule = (gf' - fg') / g^2.

Never been a huge fan of "top times bottom" chants and all that stuff. Also, it would be nice if Mr. Burger simplified some of the problems sometimes when he gets to the end. It's nice to say well we're done, but technically you're not unless multiplying everything out would be ridiculously complicated.

At any rate though, his teaching style is still very effective and helps to keep me focused when I'm drifting in my calculus book.

Below are the descriptions for each of the lessons included in the series:

Supplementary Files: