Page 72 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

VED1
E L-LOVELY-H math3-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

noEPk;soh dk rfDs

B'N dk ;hwKs wkB (limiting value), x d/ ;kg/y f (x) dk fBy/VB^r[DKe iK fBy/VBk
(differential coefficient) ejkT[Adk j?.
x
dy df ()
y′
fNZgDh 1H ;XkoD o{g s'A fBy/VB^r[DKe (differential coefficient) B{z ,, y, ,
dx 1 dx
d
fx ′ ( ),D ( ), f ′ nkfd ;ze/sK s'A gqrN eod/ jK.
fx
( ), f x
dx
fNZgDh 2H fe;h cbB d/ fBy/VB^r[DKe (differential coefficient) B{z gsk eoB dh ftXh B{z
cbB dk fBy/VB eoBk (differentiating the function) efjzd/ jB.
fJ; soQk n;hA d/yd/ jK fe fBy/VB dh ftXh ftZu uo gd (steps) j[zd/ jBL
gfjbk gd^x B{z x + δx ftZu pdbDk ns/ f (x + δx) gsk eoBk.
d{ik gd^ nzso f (x + δx) – f (x) gsk eoBk.
( + ´ ) −
()
fx x fx
fsZik gd^nzso B{z δx Bkb tzvDk ns/ fJ; soQK gsk eoBk.
´x
( + ´ ) −
fx x fx
()
u"Ek gd^id'A δx Iho' d/ tZb/ nZr/ tZXdk j? T[d'A nB[gks dh ;hwk gsk
´x
eoBk.
fNZgDh^fJZE'A nZr/ x dk tkXk δx d/ ;EkB s/ h fbfynk ikJ/rk sKfe ftfdnkoEh δ ns/ x dh
d[ftXk ftZu Bk oj'. fJ; bJh i/eo f (x), x dk e'Jh cbB j? sK
( + ) −
fx h fx
()
lim
h→ 0 h
B{z f (x) dk fBy/VB^r[DKe efjzd/ jB. fJj fXnkB ftZu oZyDk ukjhdk j? fe T[go'es ftnzie B{z
h dk cbB wzfBnk iKdk j? Gkt h B{z uo wzfBnk iKdk j? ns/ x B{z nuo.

3H3 fe;h nuo okPh dk fBy/VB^r[DKe
(Differential Coefficient of a Constant)

wzB fbU c e'Jh nuo okPh j?. fJ; bJh fJZE/ f (x) = c j[D x d/ ;ko/ wkBK d/ bJh nuo okPh
ftZu e'Jh gfotosB BjhA j' ;edk.

fJ; soQK nuo okPh dk fBy/VB^r[DKe Iho' j[zdk j?.

3H4 nuo okPh ns/ cbB d/ r[DBcb dk fBy/VB^r[DKe (Differential
Coefficient of the Product of a Constant and a Function)

wzB fbU fe a e'Jh nuo okPh j? ns/ f (x) fdZsk j'fJnk cbB j?, sK

66 LOVELY PROFESSIONAL UNIVERSITY