Quotient Rule Example

Real Player Webvideos

1. [Play Video]  2 minutes: Product and Quotient Rules for Differentiation. Statement Only

Differentiation of Rational Functions

[Play Video]  4 minutes:  Using the Quotient Rule, Example with linear expression and quadratic as numerator and denominator.

A Rational function has the form  f(x) = p(x)/q(x) where p(x) and q(x) are polynomials.  The sum, difference, products and quotients of rational functions are also rational functions. Their derivatives can be found from the differentiation rules for polynomials combined with differentiation rules for  the product, sum, differences and quotients of functions.

www.whyslopes.com
More Calculus
[ Back ] [ Up ] [ Next ]

For  help in calculus, explore
Volumes 2. Three Skills for Algebra and 3. Why Slopes & More Math, and  Calculus Introduction site area. See how to learn or teach key skills and concepts, some not all.

Calculus Videos
0.   First Calculus Preview
0. Triangle Inequality
0 Inequalities
0. Solving Inequalities
1. Distance+Midpt Formulas
1. Function Domains
1.Polynomial Domain+Range
1. Fn:  Linear Combinations
1. Fn Composition II
1. Fn Composition I
1. Solving y**n = x**m
2 .Real Numbers
2. Limits Numerical View
2. Limits,. Formal Definition
2. Limit Properties Numerically
2. Decimal View of Limits
2. Error Control View
2. Limits & Continuity
2. Limit Vals via Substitution
2. Limits & Composite Fns
2.. Limit Examples
2. One Sided Limits
2. Infinity and Limits
2. Parameters in Limits
3. Derivative Motivation
3.  Derivative Definition I
3. Derivatives Definition II
3. Calculus: Why Radians
3 d/dx of sin(x) & cos(x)  (I)
3 d/dx of sin(x) & cos(x) (II)
3.Sum Rule
3. Product Rule
3. Power Rule
3. Previous Rules Combined
3. d/dx for Polynomials
3. Reciprocal Rule
3. Reciprocal Law: sec & csc
3. Reciprocals & Power Rule
3. Power Law for Integers < 0
3. Quotient Rule
3. Quotient Rule Examples
3. Quotient Rule: tan & cot
3.  Linear Chain Rule
3. Chain Rule for Powers
3. Chain Rule - Polynomials
3. Chain Rule Examples I
3. Chain Rule Examples II
3. Linear Approximation I
3. General Chain Rule
3. Inverse Fns Derivatives
3. Chain Rule: ln(x) & exp(x)
3. Square & Cube Roots
4.  Linear Approximation
4. Second Derivative Test
4. Sketch y = x^3 - 6x^2- 12x
4. Sketch y = x^3 - 3 x^2 - 9x
4. Sketch y = 1 - 1/(1+x^2)
5. Indefinite Integrals A
5. Indefinite Integrals B.
5  Indefinite Integrals C
6. Definite Integral D
6. Area Under Curves
7. Volume of a Sphere

To Learn More, visit Volumes 2 and 3.

Advanced Topics

Limit Properties Algebraically
Pigeon Hole Principle
Bolzano
Constant Difference Thm
Continuous Functions
Rational Functions
Mean Value Theorem
One Side Range Theorem
Range On One Side
From Lipschitz Continuity

To Learn More: Visit Real Analysis.

[ Back ] [ Up ] [ Next ]

[ Back ] [ Up ] [ Next ] [Top of this Page]  
Road Safety Message  Do not walk on a road with your back to the traffic. 
  Favourite Sites:  BBC News  and mathematics portion of  English National Curriculum  
[Site Author Contact Form]  If you find an error, please cut and paste its 
web page location (URL) into its report.

All trademarks and copyrights on this page are owned by their respective owners.
Copyright to comments & contributions are owned by the Poster. 
The Rest © 1995 onward by site author,   Alan Selby (email) All Rights Reserved. 
www.whyslopes.com