I-Calculus
14 - Product Rule
Let
y
=
f
(
x
)
g
(
x
)
, then
d
y
d
x
=
lim
h
→
0
f
(
x
+
h
)
g
(
x
+
h
)
−
f
(
x
)
g
(
x
)
h
=
lim
h
→
0
f
(
x
+
h
)
g
(
x
+
h
)
−
f
(
x
)
g
(
x
+
h
)
+
f
(
x
)
g
(
x
+
h
)
−
f
(
x
)
g
(
x
)
h
=
lim
h
→
0
f
(
x
+
h
)
g
(
x
+
h
)
−
f
(
x
)
g
(
x
+
h
)
h
+
f
(
x
)
g
(
x
+
h
)
−
f
(
x
)
g
(
x
)
h
=
lim
h
→
0
f
(
x
+
h
)
g
(
x
+
h
)
−
f
(
x
)
g
(
x
+
h
)
h
+
lim
h
→
0
f
(
x
)
g
(
x
+
h
)
−
f
(
x
)
g
(
x
)
h
=
lim
h
→
0
[
f
(
x
+
h
)
−
f
(
x
)
]
g
(
x
+
h
)
h
+
lim
h
→
0
f
(
x
)
[
g
(
x
+
h
)
−
g
(
x
)
]
h
=
lim
h
→
0
f
(
x
+
h
)
−
f
(
x
)
h
lim
h
→
0
g
(
x
+
h
)
+
lim
h
→
0
f
(
x
)
lim
h
→
0
g
(
x
+
h
)
−
g
(
x
)
h
=
f
′
(
x
)
g
(
x
)
+
f
(
x
)
g
′
(
x
)
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