Ex 3_2 - 7 44 c hapter : D jfferentiarjoi 3 The s ymbol D...

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744 chapter 3: Djfferentiarjoi I How to Read the Symbots for r' ) double p.lDc_ , 1/squrcrll'rrsquarcd" r" 'l rriplcDrirnc' F -rl r. are r offby drtothe," EXERCISES 3.2 In Excnscs I 12. lnd the firstdd second deivatires 1. r: 321 1zj +21.> f.,: zrr+] 10.r=4 1r-rr .. t2 I I d B' H1 In tir€rciscs 13 16, find _f (a) by applying rhe producr Rutc and (b) by nultiDlyins the fadors to prcduce a sum of simpler tems to 13. r= (.1 r:)(rr r+1) 11.r,:(' l)(rr+r- t) The symbol D'?means the opcration ofdifferenti,ttion is performed t$,ice. Ifl, = i6, then r,' = 615 andre have ,, .ry d.- r'=;:./.a(,'1 =3orr' Thus D.(.n.) : 3&r. If)" is differentiablc, its derivative, t"' : dl."/dj = ./rr/.*r is the third dern of-r wiih respect tor. Thc names continue as ]ou imagine. widr ,at = tLs,, l d,,, - at' ,tt = D"t- denoting the,th derivative of r $idr respcct to -r for any positive integer r. We can interprctihe second derivarivc as the rate ofchange ofrhe slope ofthe l]: b the graph of-L = /(r) at each po t. V,u 'vill see in rhe ncxt chapler rhal thc secor,: fllahve rcveals whcthcr
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Ex 3_2 - 7 44 c hapter : D jfferentiarjoi 3 The s ymbol D...

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