Answers and Explanations 483
Answers
701–800
779.
2
1
e
e +
Using the definition of hyperbolic cosine gives you the following:
sech
cosh
1
2
1
1
2
2
2
2
1
1 2
1 2
1 2
1
0
=
=
+
= +
= +
−
e
e
e
e e
e
e
780.
2 cosh x sinh x
The given function is y = cosh
2 
x, which equals (cosh x)
2
. Using the chain rule
gives you the derivative y′ = 2 cosh x sinh x.
781.
2
2
x
x
cosh ( )
The given function is y
x
=
( )
sinh
2 . Using the chain rule gives you
′ =
( )
(
) ( )
=
( )
y
x
x
x
x
cosh
cosh
2
2
2
2
782.
−
( )
( )
1
3
2
2
csch
coth
x
x
Here’s the given function:
y
x
=
( )
1
6
2
csch
Use the chain rule to find the derivative:
′ =
−
( )
( )
(
)( )
= −
( )
( )
y
x
x
x
x
1
6
2
2
2
1
3
2
2
csch
coth
csch
coth
783.
e
e
x
x
sech
2
( )
Here’s the given function:
y
e
x
=
( )
tanh
Use the chain rule to find the derivative:
′ =
( )




=
( )
y
e
e
e
e
x
x
x
x
sech
sech
2
2