Lecture Note Differentiation
28 enAkñúgeragcRkmYy plitplRbcaMéf¶KW QK( )= 1 12 EdlKtag[vinieyaK
mUlFnrbs;Rkumh‘un. ):an;sμankMeNInCaPaKryénvinieyaKmUlFnEdlRtUvkar edIm,IbegáIn
plitpl 1.2PaKry. (At a certain factory, the daily output is ()
, 200K Ékta
QK=1, 200K^12
units, where Kdenotes the firm’s ent. Estimate the percentage
increase in capit investment that is needed to produce a 1.2 percent increase in
output.)
capital investm
al
9 ]bmafaéføedImsrubKitCaduløaelIkarplitqÉktaKWCq( )=++ 3 q q^2500.
:an;sμanéføedImelIk a
ar
2
k> eRbIkarviPaK m:aCINl edIm,I) arplitÉkt I 41.
x> KNnaéføedImCak;EsþgelIkarplitÉktaTI 41.
(Suppose the total cost in dollars of manufacturing q units is
00. a/. Use m ginal analysis to estimate the cost of
manufacturing the 41th unit. b/. Compute the actual cost of manufacturing the
41th.)
T
Cq()=++ 3 q q^25
30 éføedImsrubrbs;plitkrmñak;kMNt;edayCq( )=0.1q^32 −++0.5q 500 q 200 duløa
Edl
k Ik itÉktaTI 4.
manufacturer’s tota
qCacMnYn ÉktaEdlRtUvplit.
eRbIkarviPaKm:aCINl edIm,I):an;sμanéføedIm,Iel arpl
x> KNnaéfø edImCak;EsþgelIkarplitÉktaTI4.
(A l cost is Cq( )=−++0.1q^32 0.5q 500 q 200 dollars,
q is the number of units produced. a/. Use marginal analysis to estimate the cos
of manu
where
t
facturing the 4th unit. b/. Compute the actual cost of manufacturing the
th
31 erivative
4 unit.)
Use the chain rule to compute the d
dy
dx
and simplify your answer.
a.yu u x=^2 +=−1, 3 2 b.yuu u x=25,1^22 −+ =−
c.yuux x= ,23=+−^2 d. 2 2
1
yu,
u
= =+x (^1)
e.yux^1 ,9^22 ,^1
u
= =− f.
1
yuu
x
==
−
ifferentiate the following function
/. ()
32 D
a 2
1
41
fx
x
=
+
b/. ()
()
2 4
3
1
fx
x
=
−
c/. ()( )
5
f xx=+ 13
33 R)ak;cMNUlRbcaMqñaMsrubénRkumh‘unmYyKWft()=++ 10 t t^2236 Ban;duløa kñúgry³eBl
qañM eRkayBI karbegáItenAkñúgExmkraqñaM 1988.
k> etIenAkñúgExmkraqñaM 1992 R)ak;cMNUlsrub rbs;Rkumh‘unnwgekInkñúg GRtab:unμan?
t