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- Politecnico di Milano
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- Energy Engineering
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- Analisi e geometria 2
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18 Derivate parziali e direzionali
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Analisi e geometria 2By topic
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LEZIONE18. 2.5.2023 DERIVAZIONEin M RiordiamoinR y= f(x) rapportoincrementale Al ann- d * a h+ 0 se 7finta -seff-angolarerettetangente-tanL Fute" f:D(1RM)-IR aperto acD,tan Xf= f(a+t)- f(c) ebnon hasenso dividerepertoretore -Z Iapproccio .....- z= Y(x)incrementsseparatamlecomponentidi In12,2= (a,b)cD 4(x)= f(x,b) iI I teniamofissey= b e y incrematiano a 2x -x(a- +,a+ T) y=b 4(a)-- - 4(a)- he-f(c,b)= sefinite(a,b)derirateparzialedifrispettoadele (fa(a,b),Daf(,b))Significatogemetrico:sefficienteangolarerettetargentealgraficdz = 4(x)Sub pianoy=b Analogamentedefinisco f(a,b)(fy(a,b),Dyf(x,b) - -frait Out DEF.Ilvettore(fx(a,b),fy(,b))= = Xf(c,b)eil GRADIENTEdifin(2,b) Es.1. f(x,y)=ay+ 3sixy trovarefor,fyeiff in(1,2) 4(x)= f(x,2)= 4x+3 in (22) 4'(x)= 12x +6Ces(ex 4(()=12 + 6c2 == (1,2) 4(y)=..-- (1,2)= 4 + 30x2 Xf(1,2)= (22+ 622,4+ 32x2)
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