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VED1
E L-LOVELY-H math3-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

fJekJh^3 L fBy/VB

y δ dy B'N
s'A puD d/ bJh fejk iKdk j? fe cbB dk x d/ ;kg/y fBy/VB^r[DKe lim B{z (y)
x δ→ 0 x δ dx
dy
iK fbyd/ jB. fJ; soQK ;hwk gskeoB dh fJ; fefonk B{z fBy/VB eoBk efjzd/ jB
dx
iK fe;h cbB d/ fBy/VB^r[DKe gsk eoB dh fefonk B[z fBy/VB (Differentiation) efjzd/
jB.
• i/eo x dk e'Jh cbB f (x) ns/ x + δx dk T[jh cbB f (x + δx) j't/ sK
δ
(
(
fx + x)- fx)
lim dk ;hwKs wkB (limiting value), x d/ ;kg/y f (x) dk
´ x+0 δ x
fBy/VB^r[DKe (differential coefficient) ejkT[Adk j?.
d d d
x
• { ()} = f 1 () ± f 2 ()
fx
x
dx dx dx
• fJ; soQK d' cbBK d/ i'V iK nzso dk fBy/VB^r[DKe T[jBK d/ fBy/VB^r[DKe d/ i'V iK
nzso d/ pokpo j[zdk j?.
d
e
• () = e
x
x
dx
d
• a = a x log a Gkt d' cbBK d/ Gkrcb dk fBy/VB^r[DKe (Diff. Coeff.)
x
dx e

3H13 Ppde'P (Keywords)
• fBy/VB^r[DKe (Differential Coefficient) ^ ntebi.
• tkXk (growth) ^ tkXk.

3H14 nfGnk; gqPB (Review Questions)

d
−
2
x
1H (6 ) dk wkB eZY'. (T[Zso L –12x)
dx
d
5
6
2H (5x + 2 ) x dk wkB eZY'. (T[Zso L 30x + 2)
dx
d
x
3H f;ZX eo' fe a =a x log a H
dx e
6 1 1
4H 6 logx − x − 7 dk fBy/VB r[DK gsk eo'. (T[Zso L − x )
2
x 2
x dy
5H i/eo y= sK ;kfps eo' fe x = y (1 y− ) .
x+ 5 dx

T[Zso L ;t?^w[bKeD (Answer: Self Assessment)
6
1H (i) fBy/VB (ii) r[DBcb (iii) a (v) n – 1 (v) 63x
2H (i) (a) (ii) (b) (iii) (c) (iv) (d) (v) (a)

LOVELY PROFESSIONAL UNIVERSITY 79