Answers and Explanations 485
Answers
701–800
788.
2x
3
– x
Before taking the derivative, simplify the function:
y x
x
x e
e
x
e
e
x
x
x
x
=
( )
=
−
=
− ( )
−
−
3
3
3
1
2
2
sinh ln
ln
ln
ln
ln
=
−
=
−
−
x x x
x
x
3
1
4
2
2
1
2
1
2
Now simply take the derivative using the power rule:
′ = ( ) − ( )
=
−
y
x
x
x
x
1
2
4
1
2
2
2
3
3
789.
1
3
3
3
csch sech
x
x
The given function is
y
x
=
( )
ln tanh 3
Use the chain rule to find the derivative:
′ =
( ) (
)( )
y
x
x
1
3
3
1
3
2
tanh
sech
Rewrite and simplify the equation to get the answer:
′ =
=
y
x
x
x
x
x
1
3
3
3
1
3
1
3
1
3
1
3
2
cosh
sinh
cosh
sinh
cosh
= = 1
3
3
3
csch sech
x
x
790.
−
−
(
)+
1
3
1 3
cosh
x C
Here’s the given problem:
sinh 1 3
−
(
)
∫
x dx
Answers
701–800
788.
2x
3
– x
Before taking the derivative, simplify the function:
y x
x
x e
e
x
e
e
x
x
x
x
=
( )
=
−
=
− ( )
−
−
3
3
3
1
2
2
sinh ln
ln
ln
ln
ln
=
−
=
−
−
x x x
x
x
3
1
4
2
2
1
2
1
2
Now simply take the derivative using the power rule:
′ = ( ) − ( )
=
−
y
x
x
x
x
1
2
4
1
2
2
2
3
3
789.
1
3
3
3
csch sech
x
x
The given function is
y
x
=
( )
ln tanh 3
Use the chain rule to find the derivative:
′ =
( ) (
)( )
y
x
x
1
3
3
1
3
2
tanh
sech
Rewrite and simplify the equation to get the answer:
′ =
=
y
x
x
x
x
x
1
3
3
3
1
3
1
3
1
3
1
3
2
cosh
sinh
cosh
sinh
cosh
= = 1
3
3
3
csch sech
x
x
790.
−
−
(
)+
1
3
1 3
cosh
x C
Here’s the given problem:
sinh 1 3
−
(
)
∫
x dx