Answers and Explanations 471
Answers
701–800
750.
2
2
2
x x
−
To find the derivative of y
x
=
−
(
)
−
2
1
1
sin
, use the derivative formula for sin
−1
x and the
chain rule:
′ =
− −
(
)
=
−
−
+
(
)
=
−
y
x
x
x
x x
2
1
1
1
2
1
2
1
2
2
2
2
2
751.
−
−
− −
− +
12
3
2
1
3
8
5
2
x
x
x
x
To find the derivative of y
x
x
=
+
−
3
1
4
cos (
), you need to know the derivative formula
for the inverse cosine function and also use the chain rule:
′ = −
−
+
(
)










+
(
)
=
−
+
(
)
−
+
+
=
−
y
x
x
x
x
x
x
x
3
1
1
4
1
3 4
1
1
2
1
4
2
3
3
8
5
2
(
)
2 2
3
2
1
3
8
5
2
x
x
x
x
−
− −
− +
752.
1
2
1
1
2
tan
−
+
(
)
x
x
First rewrite the radical using an exponent:
y
x
x
=
= (
)
−
−
tan
t an
1
1
1 2
Then use the derivative formula for tan
−1 
x and the chain rule to find the derivative:
′ = (
)
+




=
+
(
)
−
−
−
y
x
x
x
x
1
2
1
1
1
2
1
1
1 2
2
1
2
tan
tan
753.
1
1
1
2
−
−
−
x
x
x
sin
First rewrite the radical using an exponent:
y
x
x
x
x
= −
= −
(
)
−
−
1
1
2
1
2
1 2
1
sin
s in