744
chapter
3: Djfferentiarjoi
I
How
to Read
the Symbots
for
r'
)
double
p.lDc_
,
1/squrcrll'rrsquarcd"
r"
'l
rriplcDrirnc'
F
rl
r. are
r offby drtothe,"
EXERCISES
3.2
In Excnscs I 12.
lnd the firstdd second
deivatires
1. r:
321
1zj +21.>
f.,:
zrr+]
10.r=4
1rrr
..
t2
I
I
d
B'
H1
In tir€rciscs
13 16,
find
_f
(a) by applying
rhe
producr
Rutc
and
(b) by nultiDlyins
the
fadors
to prcduce
a sum
of simpler
tems
to
13.
r=
(.1
r:)(rr
r+1)
11.r,:('
l)(rr+r
t)
The symbol D'?means
the opcration ofdifferenti,ttion
is performed
t$,ice.
Ifl,
=
i6, then r,'
=
615 andre have
,,
.ry
d.
r'=;:./.a(,'1
=3orr'
Thus D.(.n.)
:
3&r.
If)" is differentiablc,
its derivative,
t"'
:
dl."/dj
=
./rr/.*r is the
third dern
ofr wiih respect
tor. Thc names
continue
as
]ou
imagine.
widr
,at
= tLs,, l
d,,,

at'
,tt
=
D"t
denoting
the,th derivative
of r $idr respcct
to
r
for any positive
integer
r.
We can
interprctihe
second
derivarivc
as
the
rate ofchange
ofrhe slope
ofthe
l]:
b the graph ofL
=
/(r)
at each po t. V,u
'vill
see
in rhe ncxt chapler
rhal
thc secor,:
fllahve rcveals whcthcr