Part II: The Answers
472
Answers
701–800
Find the derivative using the product rule and the derivative formula for sin
−1 
x:
′ =
−
( ) −
( )
+ −
( ) −
= −
−
+
−
−
−
−
y
x
x
x
x
x
x
x
x
x
1
2
1
2
1
1
1
1
1
1
2
1 2
1
2
1 2
2
1
2
2
sin
sin
− −
= −
−
−
x
x
x
x
2
1
2
1
1
sin
754.
−
+
sin
cos
x
x
1
2
To find the derivative of y
x
=
(
)
−
tan cos
1
, use the derivative formula for tan
−1
x along
with the chain rule:
′ = + (
)
−
(
)=
−
+
y
x
x
x
x
1
1
1
2
2
cos
sin
sin
cos
755.
e
t t
t
sec
−
−
1
2
1
Find the derivative of y e
t
=
−
sec
1 using the chain rule and the derivative formula for
sec
−1 
t:
′ =
−
=
−
−
−
y e
t t
e
t t
t
t
sec
sec
1
1
1
1
1
2
2
756.
−
−
2
1
4
e
x
To find the derivative of y = csc
−1
e
2x
, use the derivative formula for csc
−1
x along with
the chain rule:
′ =
−
( ) −
( ( ))
=
−
−
y
e
e
e
e
x
x
x
x
1
1
2
2
1
2
2
2
2
4
757.
e
x
x
x
x
sec
sec
−
−
+
−






1
1
2
1
1
To find the derivative of y e
x
x
=
−
sec
1 , use the derivative formula for e
x
along with the
chain rule and product rule:
′ =
+
−

 

 
=
+
−

 


−
−
−
−
y e
x x x x
e
x
x
x
x
x
x
sec
sec
sec
sec
1
1
1
1
1
1
1
1
2
1
2
 