The concept of a limit or limiting process, essential to the understanding of calculus, has been around for thousands of years. In fact, early mathematicians used a limiting process to obtain better and better approximations of areas of circles. Section 3-1: The Definition of the Derivative. In the first section of the Limits chapter we saw that the computation of the slope of a tangent line, the instantaneous rate of change of a function, and the instantaneous velocity of an object at (x = a ) all required us to compute the following limit. Derivative (calculus) synonyms, Derivative (calculus) pronunciation, Derivative (calculus) translation, English dictionary definition of Derivative (calculus). Resulting from or employing derivation: a derivative word; a derivative process.

2.2 Definition Of Derivativeap Calculus Algebra
2.2 Definition Of Derivativeap Calculus Calculator

For y = 1/(2x + 3) use the limit definition of derivative to calculate y. For y = 1/(2 x + 3) use the limit definition of derivative to calculate y'. If you input an x into f prime, you're getting the slope of the tangent line at that point. Now, another notation that you'll see less likely in a calculus class but you might see in a physics class is the notation y with a dot over it, so you could write this is y with a dot over it, which also denotes the derivative. You might also see y prime.

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de·riv·a·tive

(dĭ-rĭv′ə-tĭv)adj.

1. Resulting from or employing derivation: a derivative word; a derivative process.

2. Copied or adapted from others: a highly derivative prose style.

2. Linguistics A word formed from another by derivation, such as electricity from electric.

3. Mathematics

a. The limiting value of the ratio of the change in a function to the corresponding change in its independent variable.

b. The instantaneous rate of change of a function with respect to its variable.

c. The slope of the tangent line to the graph of a function at a given point. Also called differential coefficient, fluxion.

4. Chemistry A compound derived or obtained from another and containing essential elements of the parent substance.

2.2 Definition Of Derivativeap Calculus Algebra

5. A financial instrument that derives its value from another more fundamental asset, as a commitment to buy a bond for a certain sum on a certain date.

American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

derivative

(dɪˈrɪvətɪv) adj

2. based on or making use of other sources; not original or primary

3. copied from others, esp slavishly; plagiaristic

4. a term, idea, etc, that is based on or derived from another in the same class

5. (Linguistics) a word derived from another word

6. (Chemistry) chem a compound that is formed from, or can be regarded as formed from, a structurally related compound: chloroform is a derivative of methane.

7. (Mathematics) maths

2.2 Definition Of Derivativeap Calculus Calculator

a. Also called: differential coefficientorfirst derivative the change of a function, f(x), with respect to an infinitesimally small change in the independent variable, x; the limit of [f(a + Δx)–f(a)]/Δx, at x = a, as the increment, Δx, tends to 0. Symbols: df(x)/dx, f′(x), Df(x): the derivative of xⁿ is nx^n–1.

b. the rate of change of one quantity with respect to another: velocity is the derivative of distance with respect to time.

8. (Banking & Finance) finance

a. (usually plural) a financial instrument, such as a futures contract or option, the price of which is largely determined by the commodity, currency, share price, interest rate, etc, to which it is linked

9. (Psychoanalysis) psychoanal an activity that represents the expression of hidden impulses and desires by channelling them into socially acceptable forms

Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

de•riv•a•tive

(dɪˈrɪv ə tɪv)
adj. n.

2. something derived.

3. a word that has undergone derivation from another, as atomic from atom.

4. a chemical substance or compound obtained or regarded as derived from another.

5. Math. the instantaneous rate of change of one quantity in a function with respect to another.

6. a financial contract whose value derives from the value of underlying stocks, bonds, currencies, commodities, etc.

de•riv′a•tive•ly,adv.

de·riv·a·tive

(dĭ-rĭv′ə-tĭv)

In calculus, the slope of the tangent line to a curve at a particular point on the curve. Since a curve represents a function, its derivative can also be thought of as the rate of change of the corresponding function at the given point. Derivatives are computed using differentiation.

The American Heritage® Student Science Dictionary, Second Edition. Copyright © 2014 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

Noun	1.	derivative - the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx derived function, differential, differential coefficient, first derivative curvature - the rate of change (at a point) of the angle between a curve and a tangent to the curve figuring, reckoning, calculation, computation - problem solving that involves numbers or quantities partial, partial derivative - the derivative of a function of two or more variables with respect to a single variable while the other variables are considered to be constant
2.	derivative - a compound obtained from, or regarded as derived from, another compound chemical compound, compound - (chemistry) a substance formed by chemical union of two or more elements or ingredients in definite proportion by weight
3.	derivative - a financial instrument whose value is based on another security legal document, legal instrument, official document, instrument - (law) a document that states some contractual relationship or grants some right futures contract - an agreement to buy or sell a specific amount of a commodity or financial instrument at a particular price on a stipulated future date; the contract can be sold before the settlement date law, jurisprudence - the collection of rules imposed by authority; 'civilization presupposes respect for the law'; 'the great problem for jurisprudence to allow freedom while enforcing order' option - the right to buy or sell property at an agreed price; the right is purchased and if it is not exercised by a stated date the money is forfeited
4.	derivative - (linguistics) a word that is derived from another word; '`electricity' is a derivative of `electric' word - a unit of language that native speakers can identify; 'words are the blocks from which sentences are made'; 'he hardly said ten words