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EXAMPLE 4
Differentiating the Reciprocal of a Function
(a)
d
d
x
(
1
x
2
+
x
)
=
−
d
d
x
(
x
2
+
x
)
(
x
2
+
x
)
2
=
−
2
x
+
1
(
x
2
+
x
)
2
↑
Use (1).
(b)
d
d
x
e
−
x
=
d
d
x
(
1
e
x
)
=
−
d
d
x
e
x
(
e
x
)
2
=
−
e
x
e
2
x
=
−
1
e
x
=
−
e
−
x
↑
Use (1).
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