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Topic: Product rule

In the News (Tue 18 Jun 13)

 Product rule The product rule, of calculus, governs the differentiation of products of differentiable functions. One special case of the product rule is the Constant Multiple Rule which states: if c is a real number and f(x) is a differentiable function, then cf(x) is also differentiable and it derivative equals c multiplied by the derivative of f(x). The product rule can be used to derive the rule for integration by parts and the quotient rule. www.ebroadcast.com.au /lookup/encyclopedia/pr/Product_rule.html   (571 words)

 Product rule - Wikipedia, the free encyclopedia In mathematics, the product rule of calculus, also called Leibniz's law (see derivation), governs the differentiation of products of differentiable functions. and this is indeed the differential form of the product rule. One special case of the product rule is the Constant Multiple Rule which states: if c is a real number and f(x) is a differentiable function, then cf(x) is also differentiable, and its derivative is (c × f)'(x) = c × f '(x). en.wikipedia.org /wiki/Product_rule   (591 words)

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 PlanetMath: zero rule of product For elements of an integral domain, a product equals to zero if and only if at least one of the factors equals to zero. "zero rule of product" is owned by pahio. This is version 3 of zero rule of product, born on 2005-03-06, modified 2005-06-26. planetmath.org /encyclopedia/ZeroRuleOfProduct.html   (65 words)

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 World Web Math: The Product Rule   (Site not responding. Last check: 2007-10-18) A good way to remember the product rule for differentiation is ``the first times the derivative of the second plus the second times the derivative of the first.'' It may seem non-intuitive now, but just see, and in a few days you'll be repeating it to yourself, too. This argument cannot constitute a rigourous proof, as it uses the differentials algebraically; rather, this is a geometric indication of why the product rule has the form it does. We can use the product rule to confirm the fact that the derivative of a constant times a function is the constant times the derivative of the function. web.mit.edu /wwmath/calculus/differentiation/products.html   (365 words)

 Final Rule: S7-13-98 The Commission must approve a proposed rule change if it finds that the rule change is consistent with the requirements of the Act, and the rules and regulations thereunder, applicable to the SRO proposing the rule change. Commenters suggest that amendments to existing derivative securities products, or amendments to new derivative securities products that are listed pursuant to the amendment to Rule 19b-4, such as splitting an index or changing the exercise style, should not require a proposed rule change pursuant to Section 19b(2) of the Act. Rule 19b-4(e) requires every self-regulatory organization (SRO) seeking to rely on Rule 19b-4(e) to file Form 19b-4(e) with the Securities and Exchange Commission (SEC) at least 5 business days after commencement of trading a new derivative securities product that is not deemed to be a proposed rule change. www.sec.gov /rules/final/34-40761.htm   (12469 words)

 PlanetMath: product rule See Also: derivative, proof of product rule, product rule, power rule, proof of power rule, sum rule Cross-references: differentiable functions, product, derivative, point, differentiable, variable, functions, states This is version 8 of product rule, born on 2002-02-24, modified 2003-08-05. planetmath.org /encyclopedia/ProductRule.html   (87 words)

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 Rule of product - Wikipedia, the free encyclopedia   (Site not responding. Last check: 2007-10-18) In combinatorics, the rule of product is a basic counting principle (a.k.a. In set theory, this multiplication principle is often taken to be the definition of the product of cardinal numbers. These sets need not be finite, nor is it necessary to have only finitely many factors in the product; see cardinal number. en.wikipedia.org /wiki/Rule_of_product   (189 words)

 product rule radicals 1 (via CobWeb/3.1 planetlab2.netlab.uky.edu)   (Site not responding. Last check: 2007-10-18) Recall that the power of a product rule is valid for rational exponents as well as integers. The power of a product rule (for the power 1/n) can be stated using radical notation. The nth root of a product is equal to the product of the nth roots. www.algebra-tutoring.com.cob-web.org:8888 /product-rule-radicals-1.htm   (288 words)

 Product Rules for Derivatives - HMC Calculus Tutorials   (Site not responding. Last check: 2007-10-18) Product Rules for Derivatives - HMC Calculus Tutorials In the Calculus and its applications we often encounter functions that are expressed as the product of two other functions, like the following examples: We illustrate this rule with the following examples. www.math.hmc.edu /calculus/tutorials/prodrule   (98 words)

 The power rule - An approach to calculus It is usual to prove the power rule by means of the binomial theorem. Since the power rule is true for n = 1, it is therefore true for every natural number. We will see in Lesson 14 that the power rule is valid for any exponent. www.themathpage.com /aCalc/rules.htm   (510 words)

 Product Overview Whitepaper   (Site not responding. Last check: 2007-10-18) The technologies of Visual Rule Studio are the direct result of a rich heritage of over twenty years of leading innovation in expert system development tools. In this sample, you can see that RULE 100 Credit Authorization is dependant on the domain attribute AuthorizeAmount which is inferred in Rules 030 and 031. Its rule group – The set of backward-chaining rules that conclude the same attribute are called the attribute’s rule group. www.rulemachines.com /Whitepapers/ProdOverviewWP.htm   (2928 words)

 Product Rule   (Site not responding. Last check: 2007-10-18) The product rule is a formal rule for differentiating problems where one function is multiplied by another. The rule follows from the limit definition of derivative and is given by Compare it with the ordinary product rule to see the similarities and differences. www.math.ucdavis.edu /~kouba/CalcOneDIRECTORY/productruledirectory/ProductRule.html   (456 words)

 Visual Calculus - Product Rule   (Site not responding. Last check: 2007-10-18) Objectives: In this tutorial, we derive the formula for finding the derivative of a product of two functions and apply this formula to several examples. After working through these materials, the student should be able to derive the product rule and apply it. LiveMath notebook which illustrates the use of the product rule. archives.math.utk.edu /visual.calculus/2/product_rule.5/index.html   (96 words)

 Problem Set - Rules of calculus - functions of one variable Rules of calculus - functions of one variable The second quiz is more extensive and is designed for you to use as a final test of your understanding of the principles presented in this section. Use the product rule and the exponent rule to find the derivative of the function: www.columbia.edu /itc/sipa/math/pset_calc_rules_func_var2.html   (312 words)

 The Product Rule   (Site not responding. Last check: 2007-10-18) Okay, here is a key rule, a rule without which calculus would just be a case of goofing around with a pile of very simple functions. Suppose that we have a function h which is obtained by multiplying together two functions f and g. ``The derivative of the product of two functions is the derivative of the first times the second plus the first times the derivative of the second." www.math.ucdavis.edu /~hass/Calculus/HTAC/excerpts/node20.html   (186 words)

 The Product Rule This task provides a geometric representation of the derivative of the product of two functions. After constructing the model, the learner can derive the formula for the Product Rule. This task was adapted from ---- (1990) Derivative of a product: Exploration 2 of concepts of calculus for middle school teachers. jwilson.coe.uga.edu /EMAT6680/Horst/product/product.html   (343 words)

 2.4.htm The Product Rule is used to find the derivative of a function that is the product of two functions, and is given below: Notice that all three of the above problems could also be done by multiplying out the function first, then taking the derivative without using the Product Rule. So we will use the Quotient Rule inside of the Product Rule. www.howardcc.edu /math/MA145/2.4/2.4.htm   (201 words)

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 Math Forum - Ask Dr. Math Archives: Chain Rule I have a question on the "chain rule" when finding the derivatives of polynomials. I think I need to use l'Hopital's Rule and the natural logarithm function to find lim (x goes to 0) [(cos (2x))^(3/(x^2))]. The Math Forum is a research and educational enterprise of the Drexel School of Education. mathforum.org /library/drmath/sets/select/dm_chain_rule.html   (195 words)

 World Web Math: The Quotient Rule   (Site not responding. Last check: 2007-10-18) Now that we've seen how the derivative of a product is found, we can extend the method to quotients. In fact, after the direct approach, we'll show how the quotient rule may be obtained from the product rule with only a little sleight of hand. So, the quotient rule for differentiation is ``the derivative of the first times the second minus the first times the derivative of the second over the second squared.'' Quite a mouthful but still useful. web.mit.edu /wwmath/calculus/differentiation/quotients.html   (260 words)

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