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Topic: Derivative (examples)

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Differential calculus

Derivative

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	Derivative - Wikipedia, the free encyclopedia
		If the second derivative is positive at a critical point, that point is a local minimum; if negative, it is a local maximum; if zero, it may or may not be a local minimum or local maximum.
		The common thread is that the derivative at a point serves as a linear approximation of the function at that point.
		Perhaps the most natural situation is that of functions between differentiable manifolds; the derivative at a certain point then becomes a linear transformation between the corresponding tangent spaces and the derivative function becomes a map between the tangent bundles.
	en.wikipedia.org /wiki/Derivative (2210 words)

	Derivative (examples) - Wikipedia, the free encyclopedia
		For more background on this topic, see derivative.
		The derivative of a constant function is zero.
		The same as the previous example, but now we search the derivative of the derivative.
	en.wikipedia.org /wiki/Derivative_(examples) (151 words)

	Partial derivative - Wikipedia, the free encyclopedia
		In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).
		Equations involving an unknown function's partial derivatives are called partial differential equations and are common in physics and engineering.
		However, if all partial derivatives exist in a neighborhood of a and are continuous there, then f is totally differentiable in that neighborhood and the total derivative is continuous.
	en.wikipedia.org /wiki/Partial_derivative (475 words)

	[No title]
		Examples: On copies (works fixed in visually perceptible form): (C) 1995 John Doe On phonorecords (for sound recordings): 1995 ABC Corp., Inc. Although not required by law, it is perfectly acceptable (and often helpful) for a work to contain a notice for the original material as well as for the new work.
		Examples of generally acceptable transfer statements are "by written agreement"; "by assignment"; "by written contract"; "by will." Do not attach copies of documents of transfer to the application.
		Examples are: "Doe Publishing Company, solely owned by John Doe" or "John Doe doing business as Doe Recording Company." Space 5 Previous registration: If no registration has been made for this version or an earlier version of this work, answer the first question "no" and leave the rest of Space 5 blank.
	www.umsl.edu /services/summer/copyrite/circ14 (1414 words)

	Carboxyl Derivative Reactivity
		Methods for converting carboxylic acids into these derivatives were shown in a previous section, but the amide and anhydride preparations were not general and required strong heating.
		Reductions of carboxylic acid derivatives might be expected to lead either to aldehydes or alcohols, functional groups having a lower oxidation state of the carboxyl carbon.
		Since relatively few methods exist for the reduction of carboxylic acid derivatives to aldehydes, it would be useful to modify the reactivity and solubility of LAH to permit partial reductions of this kind to be achieved.
	www.cem.msu.edu /~reusch/VirtualText/crbacid2.htm (3950 words)

	examples.html
		Example 1: Commutation of the covariant derivative of a vector
		Example 2: Commutation of the covariant derivative of a tensor or rank 2
		Example 7: Non-trivial invariants of the Riemann tensor that vanish
	www.astro.queensu.ca /~portugal/ftp/Riegeom/examples.html (380 words)

	EE31 Matlab Examples (Site not responding. Last check: 2007-10-13)
		Both, the approximated and the analytical derivatives of the f(x) functions are depicted for comparison purposes.
		The green curve represents the analytical derivative of the f(x) function, while te red curve is its approximation.
		In this example a = 5 and h = 0.1.
	www.eeng.dcu.ie /~ee317/Matlab_Examples/findiff/tutinfo[1].htm (2259 words)

	CPS 108 Fall 2002
		To enter derivatives into the symbolic differentiator type in ‘d(the expression, the variable with which to take the derivative with respect to).
		Derivative of a function or variable to a power d(u^c), where c is a constant
		The user must specify the variable with which the derivative must be taken with respect to, otherwise the expression will be evaluated to 0.
	www.duke.edu /~pv6/cps108/aaa/usersmanual (579 words)

	Math Help - Calculus - Derivatives - Technical Tutoring
		When we look at the definition of the derivative below, it will be easy to see that the left and right hand limits of the derivative function must match at a point in order for the derivative to exist at that point.
		Moreover, the value of the derivative must match what we expect from the limits to get a properly defined derivative at that point.
		Let's try the same calculation with the "slope form" of the definition of the derivative to be sure it gives the same result.
	www.hyper-ad.com /tutoring/math/calculus/Derivatives.html (1904 words)

	[No title]
		Give an example of a function which is not continuous at a point.
		Give an example, if possible, of a function which is one, but not the other; if it's not possible, explain why.
		In a short essay, explain the relationships between the geometric, the algebraic, and the physical interpretation of the derivative and the definite integral.
	bradley.bradley.edu /~delgado/121/F03Review.txt (1124 words)

	Derivative Shortcuts
		Notice that the derivative of a product of functions is not just the product of their derivatives; the derivative is somewhat more complex.
		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)

	Untitled Document
		Below are two more examples of graphing problems, where we can apply the derivative and second derivative to help with the sketch of the graph.
		The solutions of the equation for the derivative equal to zero give the critical values, which are substituted back into the the original function.
		The points of inflection occur at the point where the second derivative is equal to zero.
	www-rohan.sdsu.edu /~jmahaffy/courses/s00/math121/lectures/graph_deriv/diffgreg.html (1070 words)

	ipedia.com: Derivative Article (Site not responding. Last check: 2007-10-13)
		The derivative of f(x) is written in several possible ways: f′(x) (pronounced f prime of x), d/dx[f(x)] (pronounced d by d x of f of x), df/dx (pronounced d f by d x), or D
		Above, the derivative of f(x) (as defined by Newton) was described as the limit, as h approaches zero, of [f(x + h) - f(x)] / h.
		Derivative of one variable with respect to another when both are functions of a third variable: Let and.
	www.ipedia.com /derivative.html (1818 words)

	U.S. Copyright Office - Information Circular
		A “derivative work,” that is, a work that is based on (or derived from) one or more already existing works, is copyrightable if it includes what the copyright law calls an “original work of authorship.” Derivative works, also known as “new versions,” include such works as translations, musical arrangements, dramatizations, fictionalizations, art reproductions, and condensations.
		A typical example of a derivative work received for registration in the Copyright Office is one that is primarily a new work but incorporates some previously published material.
		A work that has fallen in the public domain, that is, which is no longer protected by copyright, may be used for a derivative work, but the copyright in the derivative work will not restore the copyright of the public domain material.
	www.copyright.gov /circs/circ14.html (1927 words)

	Karl's Calculus Tutor - Box 4.4x: Rules for Derivatives
		Rule 3) The derivative of the sum is the sum of the derivatives.
		Rule 6) To find the derivative of a quotient or ratio, take the denominator times the derivative of the numerator, subtract from it the numerator times the derivative of the denominator, then divide the whole thing by the square of the denominator.
		Observe that the derivative of each of the products is shown in square brackets so that you can more easily see the organization.
	www.karlscalculus.org /divrules.html (851 words)

	Mathlets: Derivative Calculator (Site not responding. Last check: 2007-10-13)
		Calculates the derivative of an expression specified using a simple expression syntax.
		The result of one derivative evaluation step will be entered back into the text input field.
		The button next to the "Variable" label displays a pop-up menu which can be used to select a variable for partial derivatives.
	cs.jsu.edu /mcis/faculty/leathrum/Mathlets/derivcalc.html (240 words)

	Untitled Document
		Graph derivative function along with the graph of the function, and test the derivability of the function at a point.
		In each example, the author asks a question to which the reader may discover the answer by experimenting with values for the parameters, and also by making calculations in the built-in calculators.
		The symbolic derivative is supplied, and step-by-step procedures for calculating the limit of the difference quotient for each example or student selection are supplied.
	www.math.metrostate.edu /welcome/wrkbk_page.htm (3205 words)

	Calculus Tutorials and Problems
		The definition of the derivative of a function in calculus is explored interactively using an applet.
		Formulas and examples of the derivatives of exponential functions, in calculus, are presented.
		Examples of the derivatives of logarithmic functions, in calculus, are presented.
	www.analyzemath.com /calculus.html (1025 words)

	Examples for chapter 5, section 4:
		The second derivative of a function is 0 [or in extreme cases, undefined] where the function has an
		In addition to being the point where the graph of function changes concavity [from up to down or vice versa], the inflection point is the point of least or most rapid decrease or increase — c.f.
		Y2(x) = the derivative of Y1 and Y3(x) as the derivate of Y2 [the second derivative of Y1] — and then graph all 3.
	www.fiu.edu /~mccoydf/buscal/54prs/54prs.htm (540 words)

	Derivative Trading Systems - Examples of Horizon in Use
		In this example we show an example of the inability of the market to predict interest rates in the future.
		In this example, we are looking at the spread between a sterling 2 years swap (Act/365, semi annualised coupon) and a USD 2 year swap (Act/360, annualised coupon).
		Using the compounding function and the edit box we manipulate the basis of the USD swap by changing the frequency from 1 year to 6 month and adjusting the number of days per year to get an accurate spread.
	www.users.zetnet.co.uk /derivs/horizon.htm (1026 words)

	Derivative Plotter - Applet Page (Site not responding. Last check: 2007-10-13)
		You are encouraged to sketch the graph of the derivative f '(x) in the same window.
		As the slider is being dragged, a piece of the tangent line to the graph of the function f(x) and the value of its slope are being dynamically displayed to show the relationship between the slope of the tangent line and the corresponding value of the derivative.
		The examples are chosen to best illuminate the geometric relationship between the graphs of f(x) and its derivative f '(x).
	www.mathdl.org /images/upload_library/4/vol4/kaskosz/derapp.html (302 words)

	Calculus I (Math 2413) - Applications of Derivatives - Critical Points (Site not responding. Last check: 2007-10-13)
		We will need to be careful with this problem. The derivative of this function doesn’t exist at t=0 and so that will be one critical point. However, we will also need to determine where the derivative is zero (provided it is of course…).
		So, we can see from this that the derivative will not exist at w=3 and w=-2. However, these are NOT critical points since the function will also not exist at these points. Recall that in order for a point to be a critical point the function must actually exist at that point.
		Now, this derivative will not exist if x is a negative number or if x=0, but then again neither will the function and so these are not critical points. If x>0 the function will exist and so the only thing we need to worry about is where the derivative is zero.
	tutorial.math.lamar.edu /AllBrowsers/2413/CriticalPoints.asp (1214 words)

	Math 134, Examples from Test #1 Lectures (Site not responding. Last check: 2007-10-13)
		In this example, and in general, we see that as h gets smaller and smaller, that is as it approaches 0, the secant lines become better approximations of the tangent line.
		Example 3: The amount of money deposited in a financial institution in savings accounts is directly proportional to the interest rate the financial institution pays on the money.
		So we compute the derivative of the marginal cost, set it equal to zero, solve to find the critical points, then evaluate these points with the second derivative of the marginal cost to confirm that we've found a minimum.
	www.math.uiuc.edu /~dcmurphy/math134/example1.html (4634 words)

	EE31 Matlab Examples (Site not responding. Last check: 2007-10-13)
		derivative (forward difference) approximations of a polynomial function f(x) (the same experimented above) in a certain point a are given with errors of different order
		· example10 - this Matlab example is a generalized version of the Findifex4.m (example4), Findifex5.m (example5), and Findifex6.m (example6) examples
		· example11 - the last example is meant to show the students how the accuracy increases with the decrease of the h step value
	www.eeng.dcu.ie /~ee317/Matlab_Examples/tutinfo[1].htm (809 words)

	Creating a LIDESC_TAGS string
		Examples of software licenses with certain characteristics - Using the form to identify example licenses and specific license clauses.
		If you deploy derivative works (internal use which is not for research and development purposes), you must make the sources available to a specific party, such as the original developer.
		If you deploy derivative works (internal use which is not for research and development purposes), you must make the sources available to the public.
	www.mibsoftware.com /librock/lidesc/tags.htm (1257 words)

	Visual Calculus - Definition of derivative
		Objectives: Now that we have defined the derivative of a function at a point, in this tutorial, we define a function which is the derivative at all points of an interval.
		We use the definition of a derivative to find the derivative of some functions.
		We have used the notation f' to denote the derivative of the function f.
	archives.math.utk.edu /visual.calculus/2/definition.12 (425 words)

	Choosing a License \| Creative Commons
		Example: Jane publishes her photograph with an Attribution license, because she wants the world to use her pictures provided they give her credit.
		Example: Sara licenses a recording of her song with a No Derivative Works license.
		More examples are available on our examples page.
	creativecommons.org /learn/licenses/examples (565 words)

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