PHY183-Lecture5

# P o ly n o m i a ls t r ig f u n ct ion s e x p o n e

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Unformatted text preview: tives from now on August 31, 2006 Physics for Scientists&Engineers 1 10 C a lc u lu s R e m in d e r ( fr o m M a t h P r im e r ) ! P o ly n o m i a ls : ! T r ig f u n ct ion s: ! E x p o n e n t i a l, lo g : ! P r o d u c t r u le : ! C h a i n r u le : August 31, 2006 E x a m p le : V e lo c it y ( 1 ) ! B e t w e e n 0 an d 1 0 s, t h e po sit io n v e ct o r o f a car o n t h e r o ad is g iv e n b y ! Q u e s t i o n : W h a t i s i t s v e lo c i t y v e c t o r ? ! A n sw e r : T ak e d e r iv at iv e dn x = nx n !1 dx d sin ( ax ) = a cos ( ax ) dx x(t ) = 17.2 m ! (10.1 m)(t / s)+(1.1 m)(t /s)2 d ax e = aeax dx d 1 ln ( ax ) = dx x v(t ) = d df ( x ) \$ ! dg( x ) \$ ( f ( x )g( x )) = ! # & g( x ) + f ( x ) # " dx % " dx & % dx y (u ( x)) ! dy dy du = dx du dx 11 August 31, 2006 dx dt d = ( 7.2 m ! (10.1 m)(t / s)+(1.1 m)(t/s) 2 ) 1 dt d d d = (17.2 m ) ! ((10.1 m)(t / s) ) + ((1.1 m)(t/s) 2 ) dt dt dt 2 = 0 ! 10.1 m/s+2 " (1.1 m)(t / s ) = !10.1 m/...
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## This note was uploaded on 03/01/2010 for the course PHY 183 taught by Professor Wolf during the Spring '08 term at Michigan State University.

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