Part II: The Answers
484
Answers
701–800
784.
cosh sech sinh
x
x
2
(
)
The given function is
y = tanh(sinh x)
Use the chain rule to get the derivative:
′ =
(
)
(
)
=
(
)
y
x
x
x
x
sech sinh
cosh
cosh sech sinh
2
2
785.
5
5
5
cosh
sinh
x e
x
( )
( )
Here’s the given function:
y e
x
=
( )
sinh 5
Use the chain rule to find the derivative:
′ =
( )
(
)( )
=
( )
( )
( )
y e
x
x e
x
x
sinh
sinh
cosh
cosh
5
5
5
5
5
5
786.
−
( )
( )
40
10
10
4
sech
tanh
x
x
Rewrite the given function:
y
x
x
=
( )=
( )
 
 
sech
sech
4
4
10
10
Then use the chain rule to find the derivative:
′ =
( )
 
  −
( )
(
)( )
= −
( )
y
x
x
x
x
4
1 0
1 0
1 0
10
40
10
3
4
sech
sech(
)tanh
sech
ta anh 10x
( )
787.
2
1
1
3
2
4
4
t
t
t
sech
+
+
Here’s the given function:
y
t
=
+
(
)
tanh 1
4
Use the chain rule to find the derivative:
′ =
+
( )
(
) +
( )
(
) ( )
=
+
+
−
y
t
t
t
t
t
t
sech
sech
2
4
1 2
4
1 2
3
3
2
4
4
1
1
2
1
4
2
1
1