Mock Gateway IV (Derivatives)
1. Suppose that
f
(
x
) =
1
x
. Use the definition of derivative to show that the derivative of
f
(
x
) at
x
= 4 is

1
16
.
2. Find the derivative:
s
=
2
t
3

1
t
+ 7 + 8
t
2
3. Find the derivative:
f
(
u
) =
1
√
u

3
√
u
+
π
4. Find the derivative:
r
=
θ
3
(
cos(
θ
)
)
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5. Find the derivative:
x
=
2 +
t

t
2
t
3

3
t
+ 1
6. Find the derivative:
y
=
√
x
2
+ 3
x

1
7. Find the derivative:
v
= cos
3
u
8. Suppose that the point (4
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 Spring '08
 Mooney
 Derivative, Vector Space

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