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EXAMPLE 7
Using the Power Rule
Find the derivative of:
(a)
y
=
x
√
2
(b)
y
=
(
x
2
+
1
)
π
Solution
(a)
We differentiate
y
using the Power Rule.
y
′
=
d
d
x
x
√
2
=
√
2
x
√
2
−
1
(b)
The Power Rule for Functions also holds when the exponent is a real number. Then
y
′
=
d
d
x
(
x
2
+
1
)
π
=
π
(
x
2
+
1
)
π
−
1
(
2
x
)
=
2
π
x
(
x
2
+
1
)
π
−
1
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