Answers and Explanations 235
Answers
301–400
Then apply the power rule to find the derivative:
f x
x
x
x
x
x
x
' ( ) = −
−
+
= − −
+
−
−
−
3
2
12
3 2 12
2
3
4
2
3
4
303.
7
2
1
2
5 2
x
x
+
Begin by multiplying the factors together:
f x
x x
x
x
x
x
( ) =
+
(
)
=
+
(
)
=
+
3
1 2
3
7 2
1 2
1
1
Then apply the power rule to find the derivative:
f x
x
x
x
x
' ( ) =
+
=
+
−
7
2
1
2
7
2
1
2
5 2
1 2
5 2
304.
−
+
4 3 2 2
5
0 1
x
x
.
.
Begin by rewriting the function using a negative exponent:
f x
x
x
x
x
( )
.
.
=
+
=
+
−
3 2
3
2
4
1 1
4
11
Then apply the power rule to each term to get the derivative:
=
−
(
) + (
)
= −
+
−
x
x
x
x
x
( )
.
.
.
.
3 4
2 1 1
4 3 2 2
5
0 1
5
0 1
f '
305.
−
+
12
7
8
10 7
x
Apply the power rule to the first two terms of f x
x
x
( ) =
+
+
−
4
8
5
3 7
/
, recalling
that the derivative of a constant is zero:
f x
x
x
' ( ) = −
(
) +
= −
+
−
4 3
7
8
12
7
8
10 7
10 7
306.
−
−
−
1
2 2
2
3
x
x
Multiply the factors and rewrite the function using exponential notation:
f x
x
x
x
x
x x
x
x
x
x
( ) =
−






+
(
)
= +
− −
=
+
−
−
−
−
1 2
1 1 2
2
2
2
3
2
2
1
2