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The document discusses the application of L'Hôpital's Rule and various mathematical functions, including logarithmic and trigonometric functions. It presents different examples and solutions related to derivatives and limits. The content appears to be a mix of mathematical expressions and explanations, likely intended for educational purposes.
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Save Successive differentiation For Later Leibnite'y
ad 5 n :
ey), Ot ath By, C,%, + Wyo ee Vz, + Yn~s Sy Vet
iM
+ Uy pap eae AS eee
} Cy v1 ar
te d= ara (oy x) + bain (loge) « Bhos Hat hae
+ (Qt ey nD ee
Sol”: y = Beos(loye) + basin (oq)
fd Min Cege)ah rbers Cope
i > my = B baos (loyx) - asin ('oqx)
: Sy + qeede ~ bsin (loqx) 4 e aicos (logx)
DA ea YO Neary
o Applying Libnita’s Fbsorem
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ty
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= log om Ji ) . Show pall (14 eth (nt iy
tyro
Given “Faby 4 tow. (et 1).
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a a
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nv
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2
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=> Yaw
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= sin (maint) + Sime thet (iat) ge een
a
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> Y= cos (msin'') « murs
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=> U-*) Sma — (en t Nay =((an an +"),
=D
> Or + (emar)ay + (ntom')4
(sho wed}
1 OF yet? Lowthat U- 2 a ae is
msin "x
Soln; J =Q
=> msin |X wh
% d; = 2 - Oy po
1 SLE 2B
> sae (6) + YM = 4)
pomsin ef
Aas ate Faw“Subject
Day yee) my
> 4) (IX?) Ay, ~ ty eb
Aplying Libnile’s soem, engine
UD) pgg EOD Sort ey,
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4
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> die dd I
=> 1 + y -2) p-2=0BD Applying Lrbwitats Taste i =
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DUM, Ome og = ( Lie +n)s
Int | mn?
=> (Ga) Snar 7 (remy, -oty oS
n [ee]
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+ '
oor ya a
Fey Sn ee
Sy g(p etter
> yj ln + y, (4) ag
? HY nal i 2m, 7 OF) Yere
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=> (it QD) Year * mV) * (daant
iy Cys. K fe + (ts oy
4 ony
me)
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i
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a
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Suceersive DIT th doncivative) ‘
@ 4=tagad® OY = OM
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On+
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a
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By = Xen, a
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t
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yee ye Utd
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A sof" TE
Gey”?!
2 find te vt donreivettivg of Bin be, 008 Yx
Sol™. Lot 4s cinks cos 4x
= [asin Gx ODS tx}
[ sino + sinte |
wit oat
sin (10% + Pe) + 250 (2 v
5
a\-
‘
\
\
oe >
cy‘supyect
= hit
Stn y eos n fds
| i aw
q Qsinxcosn) COS
ie (in a &
4 2) QOSK
4
st SIM Qy .COS*®
4
ae Gsint20s) QOS
oe (1-e0s4%) Cos
= + Cosh = cos te |
ye Le OF Ene oss)4, Bind the mt enrivativa. of y= sine
Sole Y= Sin Ty
s (in *x) .
t Lu
= Le (2sint)
+ en\t
ace -C~OH
~ 7 Rg
(1 = Leos te tae
pak
q a
oe eo 10 Ea
= q 2
; aL aol cos
Oa eae tig SF )
ee - Leosta + tee
™ ny
LY caret
aE) eee Fem
a L 2” eos (tas
(am)
ane =
gy. find Fhe nth donirtivat va of yea cost sin Lx
Sol Hye a Meosd sin ae
zt 2°%e osn( 2. vintan)
= + es cosx.(1- 0054.)
ot pcos ~ 200320084 x
; = s 1 ek * Cae Eager)‘Subject ©
cty p2% ;
=yke * (oe 2
A a
ee Ke Cee — 1 obbx
% = Cos
2 9 =
he 0X
PES Gut = e?% eotgx _
A
| erry CI3%K
de ye
= ae (Saar) x0% (a daod A»)
3
ok
a + OR 5 Mes Cie ‘Boas .
s 4 ery car OA om BF
ca ny ie L
EArWOE wen Cer ek)
The COE EA we conta
_ DM/o:
aa a Lig V2 yeas C3% ae der LA
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