Part II: The Answers
474
Answers
701–800
760.
0
Rewrite 1
x
in the given function using a negative exponent:
y
x
x
x
x
=
+
=
+
( )
−
−
−
−
−
cot
cot
cot
cot
1
1
1
1
1
1
Use the derivative formula for cot
−1
x for the first term, and use the same derivative
formula and the chain rule for the second term. Here are the calculations:
′ = −
+
+
−
+ ( )
−
( )
= −
+
+
+ ( )




= −
+
+
−
−
y
x
x
x
x
x
x
x
1
1
1
1
1
1
1
1 1
1
1
1
1
2
1
2
2
2
2
2
2
x x
x
x
x
2
2
2
2
1 1
1
1
1
1
0
+




= −
+
+
+
=
761.
2
1
2
2
+
(
)
x
Here’s the given function:
y
x
x
x
=
+ +
−
tan
1
2
1
Begin by using the derivative formula for tan
−1
x on the first term and using the
quotient rule on the second term:
′ = +
+
+
(
)( )− ( )
+
(
)
= +
+ −
+
(
)
y
x
x
x x
x
x
x
x
1
1
1
1
2
1
1
1
1
1
2
2
2
2
2
2
2 2
Then get common denominators and simplify:
′ =
+
+
(
)
+ −
+
(
)
=
+
(
)
y
x
x
x
x
x
1
1
1
1
2
1
2
2
2
2
2
2
2
2