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Topic: Quotient rule


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  Quotient - Wikipedia, the free encyclopedia
For example, in the problem 6 ÷ 3, the quotient would be 2, while 6 would be called the dividend, and 3 the divisor.
In more abstract branches of mathematics, the word quotient is often used to describe sets, spaces, or algebraic structures whose elements are the equivalence classes of some equivalence relation on another set, space, or algebraic structure.
Quotients also come up in certain tests, like the IQ test, which stands for intelligence quotient.
en.wikipedia.org /wiki/Quotient   (211 words)

  
 Quotient rule - Wikipedia, the free encyclopedia
In calculus, the quotient rule is a method of finding the derivative of a function that is the quotient of two other functions for which derivatives exist.
Students of multivariable calculus will recognize it as one of the chain rules for functions of multiple variables.
Another variation to this mnemonic is given when the quotient is written with the numerator as Hi the denominator as Ho: "Ho-dee-Hi minus Hi-dee-Ho over Ho-Ho."
en.wikipedia.org /wiki/Quotient_rule   (453 words)

  
 PlanetMath: quotient rule
The quotient rule says that the derivative of the quotient
The Quotient Rule and the other differentiation formulas allow us to compute the derivative of any rational function.
This is version 10 of quotient rule, born on 2002-05-17, modified 2002-05-18.
planetmath.org /encyclopedia/QuotientRule.html   (66 words)

  
 Quotient Rule
We must be a little careful in determining the domain of the quotient f/g: a real number x lies in the domain of f/g if and only if it is in the domain of both f and g AND g(x) is not equal to zero.
The domain of the reciprocal is the set of all points x in the domain of g for which g(x) is not zero.
The quotient rule says that the derivative of the quotient is "the derivative of the top times the bottom, minus the top times the derivative of the bottom, all divided by the bottom squared".....At least, that's one way to remember it.
oregonstate.edu /instruct/mth251/cq/Stage6/Lesson/quotientRule.html   (465 words)

  
 Derivative - LearnThis.Info Enclyclopedia   (Site not responding. Last check: 2007-10-13)
This definition is used for a partial proof of the Chain Rule.
The simplest notation for differentiation that is in current use is due to Lagrange and uses the prime, ′.
Messy limit calculations can be avoided, in certain cases, because of differentiation rules which allow one to find derivatives via algebraic manipulation; rather than by direct application of Newton's difference quotient.
encyclopedia.learnthis.info /d/de/derivative.html   (1805 words)

  
 Calculus I (Math 2413) - Derivatives - Product and Quotient Rule
The proof of this rule is shown in the Extras at the end of this document.
The proof of this rule is also shown in the Extras at the end of this document.
Let’s now work an example or two with the quotient rule.  In this case, unlike the product rule examples, we are going to be able to do some problems that we weren’t able to do prior to this point.
tutorial.math.lamar.edu /AllBrowsers/2413/ProductQuotientRule.asp   (855 words)

  
 Karl's Calculus Tutor - 4.3 Derivatives: More Rules to Live By
In words, the derivative of the quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator all over the denominator squared.
Deriving a New Rule from the Quotient Rule
In this section, we will use the quotient rule to demonstrate that this same rule holds if the power term is a negative integer.
www.karlscalculus.org /calc4_3.html   (3741 words)

  
 Search Results for rule - Encyclopædia Britannica
Rule for finding the derivative of a quotient of two functions.
When rules where violated, prisoners were put in solitary confinement also known as the 'hole'.
Brief study of the quotient rule used to compute derivative of a function.
www.britannica.com /search?query=rule&submit=Find&source=MWTAB   (426 words)

  
 Intermediate Algebra Tutorial on Simplifying Radical Expressions
We can use the product rule of radicals in reverse to help us simplify the nth root of a number that we cannot take the nth root of as is, but has a factor that we can take the nth root of.
Note that both radicals have an index number of 2, so we are able to put their quotient together under one radical keeping the 2 as its index number.
Note that both radicals have an index number of 4, so we are able to put their quotient together under one radical keeping the 4 as its index number.
www.wtamu.edu /academic/anns/mps/math/mathlab/int_algebra/int_alg_tut39_simrad.htm   (1113 words)

  
 Quotient rule   (Site not responding. Last check: 2007-10-13)
Quotient Rule, The derivativeof a quotient is the denominator times the derivative of the numerator...
The derivative of the quotient of two functions is the denominator...
In this case, it's quite convenient to note that the derivative of the numeratorand denominator are the same, so that the quotient rule reduces to...
www.wushulink.com /quotient+rule.html   (797 words)

  
 Rules of Exponents and Scientific Notation-Chapter 5 Section 1   (Site not responding. Last check: 2007-10-13)
Use the quotient rule for exponents, and define a number raised to the zero power.
Since multiplication is a fast way of adding and division is a fast way of subtracting things into differents parts, there is a similar rule for raising a quotient to a power.
(To raise a quotient to apower, raise the numerator to the power and divide by the denominator to the power).
www.rose.edu /faculty/gjackson/elealg/each5-1.htm   (783 words)

  
 [No title]
Derivatives of Quotients Since a special rule was needed for derivatives of products, it seems logical that a special rule is needed for derivatives of quotients also.
The derivative of a quotient is a quotient.
The Quotient Rule gives:  EMBED Equation.DSMT4  =  EMBED Equation.DSMT4  =  EMBED Equation.DSMT4  =  EMBED Equation.DSMT4  It is not necessary to expand the denominator, but it is necessary to simplify the numerator.
www2.scc-fl.com /mgoshaw/TextTopic10forMAC2233.doc   (2893 words)

  
 Derivative Shortcuts
While these rules are being applied to power functions and polynomials first, they work for any functions.
Notice that the derivative of a quotient of functions is not just the quotient of their derivatives; the derivative is somewhat more complex.
The derivatives of various other functions can be obtained by the chain rule and the composition of inverse functions.
www.empirenet.com /tajames/calculus/notes-derivative-shortcuts.html   (1166 words)

  
 Summary: Techniques of Differentiation
The derivative of a quotient is the derivative of the top times the bottom, minus the top times the derivative of the bottom, all over the bottom squared..
The following table summarizes the derivatives of logarithmic and exponential functions, as well as their chain rule counterparts (that is, the logarithmic and exponential functions of a function).
The following table summarizes the derivatives of the six trigonometric functions, as well as their chain rule counterparts (that is, the sine, cosine, etc. of a function).
www.zweigmedia.com /ThirdEdSite/Calcsumm4.html   (697 words)

  
 quot1
There were applications of the product rule to Ricker's model for population growth and to graphing problems.
In words, the quotient rule says that the derivative of the quotient is
We can apply the quotient rule to this function to find its derivative.
www-rohan.sdsu.edu /~jmahaffy/courses/s00/math121/lectures/quotient_rule/quotient.html   (1089 words)

  
 2.4.htm
The Quotient Rule is used to find the derivative of a function that is the quotient of two functions, and is given below:
So we will use the Quotient Rule inside of the Product Rule.
Derivative of f(x) Derivative of g(x) using the quotient rule
www.howardcc.edu /math/MA145/2.4/2.4.htm   (201 words)

  
 [No title]
We saw a couple of shortcut formulas for derivatives of complicated exponentials and logarithms which are derived from the chain rule.
Remember when differentiating implicitly that y is a function of x, and as such must be hit with the chain rule.
For L’H’s Rule: Remember that you must confirm that the limit is of the form 0/0 before differentiating and that it’s the quotient of the derivatives, not the derivative of the quotient, that matters.
www.albion.edu /mathcs/MBollman/m141f4m2.html   (415 words)

  
 2.03 The Product and Quotient Rules and Higher Order Derivatives
The Product Rule is the method to find the derivative of a function which is the product of two other functions.
The Quotient Rule is the method to find the derivative of a function which is the quotient of two other functions.
When we are using the quotient rule, make sure that the formula is followed carefully.
www.flvs.net /_students/showcase_flvs/math/apcalc/module02/2_3.htm   (905 words)

  
 Karl's Calculus Tutor - Solution to Exercise 5.2-6
and, as stated before, you will need to use both the quotient rule and the chain rule to determine them.
is the quotient of two polynomials, we need to use the quotient rule in order to find
is a quotient, and with quotients, it is sufficient to find where the numerator is zero (provided the denominator is continuous and not equal to zero at the same
www.karlscalculus.org /pr5_2-6.html   (492 words)

  
 Math Help - Calculus - Properties of Derivatives - Technical Tutoring
The quotient rule gives the derivative of one function divided by another.
The chain rule is used in the case of a function of a function, also known as a composite function or as a composition of functions.
Compostions are particularly useful in the case where a given problem has so-called chained dependencies where the quantity we wish to study is a function of a second quantity which in turn depends on a third quantity.
www.hyper-ad.com /tutoring/math/calculus/Properties_of_Derivatives.html   (569 words)

  
 Calculus I Notes, Section 3-2
The derivative of a quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.
When you need tod ifferentiate a quotient of two functions, you must follow the quotient rule.
The derivative of a quotient is the quotient of the derivatives.
www.blc.edu /fac/rbuelow/calc/nt3-2.html   (328 words)

  
 Product Rule, Quotient Rule, and Chain Rule Tutorial
By now you might be thinking that the problem could have been solved with or without the chain rule.
After all, once we have determined a derivative, it is much more convenient to "plug in" values of x into a compact formula as opposed to using some multi-term monstrosity.
The chain rule is a powerful tool of calculus and it is important that you understand it thoroughly.
www.1728.com /chainrul.htm   (367 words)

  
 Visual Calculus - Quotient Rule   (Site not responding. Last check: 2007-10-13)
Objectives: In this tutorial, we derive the formula for finding the derivative of a quotient of two functions and apply this formula to several examples.
After working through these materials, the student should be able to derive the quotient rule and apply it.
LiveMath notebook which illustrates the use of the quotient rule.
archives.math.utk.edu /visual.calculus/2/quotient_rule.4   (95 words)

  
 math134notes   (Site not responding. Last check: 2007-10-13)
To apply the quotient rule, we follow the same steps as with the product rule.
Note that if you forget the formula for the quotient rule, you can derive it by using the product rule.
You may have heard of the phrase ``take the derivative of the outside and mulitply by the derivative of the inside.'' This is equivalent to what is done in the chain rule.
www.math.uiuc.edu /~handuong/math134/notes/math134notes.html   (173 words)

  
 Calculus worksheet chapter 4 on derivatives:
Take the derivative of each piece, by quotient rule or by chain rule.
Or combine this into one fraction and then use the quotient rule.
A conical tank has a radius of 160 cm and a height of 800 cm.
home.comcast.net /~jleslie9431/derivws.html   (142 words)

  
 [No title]
13.1 ("vector functions") 8: find t-derivative of this vector-valued fn of t: ((t+1)/(t-1), t exp(2t), sec(t)) ANS We differentiate the 3 components individually the first by the quotient rule followed by simplification, the second by product rule, the third by formula (or quotient rule).
Result: 2 (-2/(t-1), exp(2 t) + 2 t exp(2 t), sec(t) tan(t)) That first component again in slow-mo: To differentiate (x+1)/(x-1) with respect to x, use quotient rule 2 [T(x)/B(x)]' = [T'(x) B(x) - T(x) B'(x)]/B(x) getting with T(x)=(x+1) and B(x)=(x-1), T'(x)=1, B'(x)=1, so result is 2 2 [(x+1)/(x-1)]' = [x-1 - (x+1)]/(x-1) = -2/(x-1).
by quotient rule (or more simply power = -1 rule with chain rule, note get two - signs which yield a + sign inside here...).
www.math.temple.edu /~wds/math127hw3s   (1169 words)

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