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Content type
User Generated
Subject
Calculus
School
University of Pittsburgh Main Campus
Type
Homework
Rating
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1/3
( )
( )
( )
( ) ( ) ( )
1
9
a Formula used for derivative : , where is a real number
0, where k is a constant
Rewrite 4 7.68 ln 10 and differentiate usi
nn
e
d
x nx n
dx
d
k
dx
g t t t g t
−
=
=
= − +
( ) ( )
(
)
( )
( )
( )
( )
( )
9
9
9
9/ 2
9
1
1
2
ng the above derivative formulas.
' 4 7.68 ln 10
4 7.68 ln 10
4 7.68 ln 10
4 7.68 ln 10
9
4 7.68 0
2
e
e
e
e
e
d
g t t t
dt
d d d
tt
dt dt dt
d d d
tt
dt dt dt
d d d
tt
dt dt dt
t et
−
−
= − +
= − +
= − +
= − +

= − +


=
( )
7 / 2 1
7 / 2 1
18 7.68
Hence, ' 18 7.68 .
e
e
t et
g t t et
−
−
−
=−

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( )
( )
( )
( ) ( )
1
1.3
4
b Formula used for derivative : , where is a real number
3
Rewrite 6 and differentiate using the above derivativ
8
nn
xx
s
d
x nx n
dx
d
ee
dx
p s s e p s
s
−
−
=
=
= − −
( )
( ) ( )
( ) ( ) ( )
( ) ( )
1.3
4
1.3
4
4 1.3
4 1 1.3 1
5 2.3
2.3
5
e formulas.
3
'6
8
3
6
8
3
6
8
3
4 6 1.3
8
3
6 1.3
2
3
7.8
2
He
s
s
s
s
s
s
d
p s s e
ds
s
d d d
se
ds ds ds
s
d d d
s s e
ds ds ds
s s e
s s e
se
s
−
−
−−
− − − −
−−
−

= − −



= − −


= − −
= − − − −
= − + −
= − + −
( )
2.3
5
3
nce, ' 7.8 .
2
s
p s s e
s
−
= − + −

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( a ) Formula used for derivative : d n ( x ) = nx n−1 , where n is a real number dx d ( k ) = 0, where k is a constant dx Rewrite g ( t ) = 4 t 9 − 7.68t e + ln (10 ) and differentiate g ( t ) using the above derivative formulas. ( ) d 4 t 9 − 7.68t e + ln (10 ) dt d d d = 4 t 9 − 7.68t e + ln (10 ) dt dt dt d 9 d d =4 t − 7.68 t e + ln (10 ) dt dt dt d d d = 4 ( t 9 / 2 ) − 7.68 t e + ln (10 ) dt dt dt 9  9 −1  = 4  t 2  − 7.68 ( et e −1 ) + 0 2  7/2 = 18t − 7.68et e −1 g ' (t ) = Hence, g ' ( t ) = 18t 7 / 2 − 7.68et e −1 . ( b ) Formula used for derivative : d n x ) = nx n −1 , where n is a real number ( dx d x e ) = ex ( dx 3 − 6 s −1.3 − e s and differentiate p ( s ) using the above derivative formulas. 4 8s d  3  p ' ( s ) =  4 − 6s −1.3 − e s  ds  8s  d  3  d d =  4  − ( 6 s −1. ...
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