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VED1
E L-LOVELY-H math5-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

Hitesh Jhanji, Lovely Professional University fJekJh^5 L d{i/ ns/ T[Zuso eqw d/ fBy/VB

fJekJh^5L d{i/ ns/ T[Zuso eqw d/ fBy/VB B'N

(Second and Higher Order Differentiation)

ftP/ t;s{ (Contents)
T[d/P (Objectives)
gq;sktBk (Introduction)

5H1 T[Zgo'Ebh dk fBy/VB (Successive Differentiation)
5H2 ;koKP (Summary)

5H3 Ppde'P (Keywords)
5H4 nfGnk; gqPB (Review Questions)
5H5 ;zdoG g[;seK (Further Readings)

T[d/P (Objectives)

fJ; fJekJh d/ nfXn?B s'A pknd ftfdnkoEh :'r j'Dr/L

• T[Zgo'Ebh fBy/VB gsk eoB ftZu.

gq;sktBk (Introduction)

dy
i/eo y, x dk cbB j? sK th x dk cbB j't/rk. fJ;d/ fBy/VB^r[DKe B{z y dk d{ik fBy/VB^
dx
r[DKe ns/ fJ;B{z fsZik fBy/VB^r[DKe dk BKt fdzd/ jB.

5H1 T[Zgo'Ebh dk fBy/VB (Successive Differentiation)

dy
i/eo, y, x dk e'Jh cbB j't/ sK x d/ ;kg/y y dk fBy/VB^r[DKe Gkt th x dk cbB j[zdk j?
dx
dy d  dy 
fi;dk fco s'A fBy/VB ehsk ik ;edk j?. d/ fBy/VB^r[DKe   B{z y dk d{ik
dx dx  dx 
fBy/VB^r[DKe efjzd/ jB, fJ;h soQK y d/ d{i/ fBy/VB^r[DKe B{z y dk fsZik fBy/VB^r[DKe
2
3
dyd yd y
efjzd/ jB. fJjBK tZy^tZy fBy/VBK B{z eqw nB[;ko , , ,..... d[nkok gqrN eod/ jB.
dx dx 2 dx 3
T[Zgo'Ebh ntebi d/ bJh gqw[Zy ;ze/sB fBwB skfbek ftZu do;kJ/ rJ/ jB^
w{b cbB y = f (x) ;XkoD ;ze/sB j'o ;ze/sB

dy
gfjbk ntebi f ′ (x), Dy, y 1
dx

2
d  dy  d y
2
d{ik ntebi   = f ′′ (x), D y, y 2

dx dx  dx 2

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