25:
1849:
is itself a derivative—the rate at which the purchasing power of money decreases—then the rate of increase of inflation is the derivative of inflation, opposite in sign to the second time derivative of the purchasing power of money. Stating that a function is
1249:
1812:
1674:
1854:
is equivalent to stating that its derivative is negative, so Nixon's statement is that the second derivative of inflation is negative, and so the third derivative of purchasing power is positive.
213:
1845:
announced that the rate of increase of inflation was decreasing, which has been noted as "the first time a sitting president used the third derivative to advance his case for reelection." Since
1540:
1456:
1406:
1356:
1306:
1123:
1115:
1707:— a fundamental property of curves in three dimensions — is computed using third derivatives of coordinate functions (or the position vector) describing the curve.
35:
550:
1747:
609:
1046:
1908:
565:
288:
1857:
Since Nixon's statement allowed for the rate of inflation to increase, his statement did not necessarily indicate price stability.
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1418:
1244:{\displaystyle {\frac {d^{3}y}{dx^{3}}},\quad f'''(x),\quad {\text{or }}{\frac {d^{3}}{dx^{3}}}.}
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861:
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249:
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1008:
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835:
830:
717:
630:
575:
1716:
1558:
891:
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471:
1079:, or the rate of change of the rate of change, is changing. The third derivative of a
1958:
871:
635:
390:
347:
1738:
625:
375:
1064:
988:
24:
1925:
1726:
734:
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42:
1060:
729:
476:
433:
122:
1722:
1807:{\displaystyle \mathbf {j} (t)={\frac {d^{3}\mathbf {r} }{dt^{3}}}}
1842:
1833:) is the position function of the object with respect to time.
18:
1841:
When campaigning for a second term in office, U.S. President
1669:{\displaystyle {\frac {d^{3}}{dx^{3}}}={\frac {d}{dx}}.}
46:
1750:
1574:
1474:
1421:
1364:
1314:
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1126:
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135:
1737:
of an object. It is, essentially, the rate at which
1806:
1668:
1534:
1450:
1400:
1350:
1300:
1243:
1109:
207:
1825:) is the jerk function with respect to time, and
1258:can be used, but the above are the most common.
208:{\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)}
1679:The third derivative is the rate at which the
1040:
8:
1933:Notices of the American Mathematical Society
1901:Differential Geometry of Curves and Surfaces
1535:{\displaystyle {\frac {d^{3}}{dx^{3}}}=24x.}
51:introducing citations to additional sources
1926:"Mathematics Is an Edifice, Not a Toolbox"
1733:is defined as the third derivative of the
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41:Relevant discussion may be found on the
1888:
1545:Now for a more general definition. Let
853:
822:
762:
643:
571:Differentiating under the integral sign
509:
463:
360:
319:
276:
121:
16:Rate of change of the second derivative
1408:. Therefore, the third derivative of
7:
117:Part of a series of articles about
14:
1782:
1752:
1741:changes. In mathematical terms:
34:relies largely or entirely on a
23:
1561:. Then the third derivative of
1185:
1164:
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1657:
1651:
1640:
1619:
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1610:
1604:
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1430:
1401:{\displaystyle f''(x)=12x^{2}}
1379:
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196:
187:
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1:
1256:notations for differentiation
502:Integral of inverse functions
1924:Rossi, Hugo (October 1996).
1351:{\displaystyle f'(x)=4x^{3}}
1451:{\displaystyle f'''(x)=24x}
920:Calculus on Euclidean space
343:Logarithmic differentiation
1981:
1714:
1301:{\displaystyle f(x)=x^{4}}
1075:is the rate at which the
654:Summand limit (term test)
1872:Derivative (mathematics)
1695:Applications in geometry
1549:be any function of
1262:Mathematical definitions
338:Implicit differentiation
328:Differentiation notation
255:Inverse function theorem
1711:Applications in physics
796:Helmholtz decomposition
1808:
1670:
1536:
1452:
1402:
1352:
1302:
1245:
1111:
1110:{\displaystyle y=f(x)}
1073:third-order derivative
930:Limit of distributions
750:Directional derivative
411:FaĂ di Bruno's formula
209:
1965:Differential calculus
1809:
1701:differential geometry
1671:
1537:
1453:
1403:
1353:
1303:
1246:
1112:
1014:Mathematical analysis
925:Generalized functions
610:arithmetico-geometric
456:Leibniz integral rule
210:
1867:Aberrancy (geometry)
1748:
1572:
1472:
1419:
1362:
1312:
1270:
1124:
1086:
1019:Nonstandard analysis
492:Lebesgue integration
362:Rules and identities
133:
47:improve this article
690:Cauchy condensation
497:Contour integration
223:Fundamental theorem
150:
1897:do Carmo, Manfredo
1804:
1705:torsion of a curve
1666:
1532:
1448:
1412:is, in this case,
1398:
1348:
1298:
1241:
1117:can be denoted by
1107:
862:Partial derivative
791:generalized Stokes
685:Alternating series
566:Reduction formulae
541:tangent half-angle
528:Cylindrical shells
451:Integral transform
446:Lists of integrals
250:Mean value theorem
205:
136:
62:"Third derivative"
1877:Second derivative
1837:Economic examples
1802:
1735:position function
1681:second derivative
1638:
1602:
1502:
1218:
1189:
1159:
1077:second derivative
1057:
1056:
937:
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898:
867:Multiple integral
803:
802:
707:
706:
674:Direct comparison
645:Convergence tests
583:
582:
556:Partial fractions
423:
422:
333:Second derivative
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97:
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1691:)) is changing.
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1463:Leibniz notation
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1108:
1069:third derivative
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877:Surface integral
820:
816:
724:
720:
680:Limit comparison
600:
596:
487:Riemann integral
440:
436:
396:L'HĂ´pital's rule
353:Taylor's theorem
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1746:
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1725:, particularly
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1023:
1009:Integration Bee
984:
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938:
911:
908:
901:
900:
882:Volume integral
817:
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805:
804:
721:
716:
709:
708:
678:
597:
592:
585:
584:
576:Risch algorithm
551:Euler's formula
437:
432:
425:
424:
406:General Leibniz
289:generalizations
271:
266:
259:
245:Rolle's theorem
240:
215:
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99:
56:
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40:
28:
17:
12:
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5:
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1798:
1794:
1790:
1784:
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1761:
1758:
1754:
1717:Jerk (physics)
1715:Main article:
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1559:differentiable
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1063:, a branch of
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1022:
1021:
1016:
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1004:List of topics
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561:Changing order
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510:Integration by
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472:Antiderivative
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45:. Please help
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2:
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1910:0-13-212589-7
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1873:
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1865:
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1848:
1844:
1843:Richard Nixon
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1557: ′′ is
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872:Line integral
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814:Multivariable
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537:trigonometric
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348:Related rates
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311:
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305:of a function
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300:infinitesimal
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1943:13 November
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982:Miscellanea
947:Specialized
854:Definitions
621:Alternating
464:Definitions
277:Definitions
1939:(10): 1108
1883:References
1852:decreasing
1727:kinematics
1553:such that
1461:or, using
969:Variations
964:Stochastic
954:Fractional
823:Formalisms
786:Divergence
755:Identities
735:Divergence
285:Derivative
236:Continuity
73:newspapers
1847:inflation
959:Malliavin
846:Geometric
745:Laplacian
695:Dirichlet
606:Geometric
191:−
138:∫
103:July 2013
43:talk page
1959:Category
1899:(1976).
1861:See also
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1308:. Then
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771:Gradient
763:Theorems
730:Gradient
669:Integral
631:Binomial
616:Harmonic
481:improper
477:Integral
434:Integral
416:Reynolds
391:Quotient
320:Concepts
156:′
123:Calculus
1723:physics
994:History
892:Hessian
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1945:2012
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