]>
The
Rules of Differentiation
Suppose
c
is a constant and
f
and
g
are differentiable functions. Unscramble the following rules.
The constant rule:
ⅆ
ⅆ
x
(
c
)
=
0
The power rule:
ⅆ
ⅆ
x
(
x
c
)
=
c
⁢
x
c
−
1
The constant multiple rule:
ⅆ
ⅆ
x
(
c
⁢
f
⁡
(
x
)
)
=
c
⁢
ⅆ
ⅆ
x
(
f
⁡
(
x
)
)
The sum rule:
ⅆ
ⅆ
x
(
f
⁡
(
x
)
+
g
⁡
(
x
)
)
=
ⅆ
ⅆ
x
(
f
⁡
(
x
)
)
+
ⅆ
ⅆ
x
(
g
⁡
(
x
)
)
The difference rule:
ⅆ
ⅆ
x
(
f
⁡
(
x
)
−
g
⁡
(
x
)
)
=
ⅆ
ⅆ
x
(
f
⁡
(
x
)
)
−
ⅆ
ⅆ
x
(
g
⁡
(
x
)
)
The product rule:
ⅆ
ⅆ
x
(
f
⁡
(
x
)
⁢
g
⁡
(
x
)
)
=
ⅆ
ⅆ
x
(
f
⁡
(
x
)
)
⁢
g
⁡
(
x
)
+
ⅆ
ⅆ
x
(
g
⁡
(
x
)
)
⁢
f
⁡
(
x
)
The quotient rule:
ⅆ
ⅆ
x
(
f
⁡
(
x
)
g
⁡
(
x
)
)
=
f
′
⁡
(
x
)
⁢
g
⁡
(
x
)
−
g
′
⁡
(
x
)
⁢
f
⁡
(
x
)
(
g
⁡
(
x
)
)
2
The chain rule:
ⅆ
ⅆ
x
(
f
⁡
(
g
⁡
(
x
)
)
)
=
f
′
⁡
(
g
⁡
(
x
)
)
⁢
g
′
⁡
(
x
)