MAT 16A Lecture Notes - Lecture 10: Quotient Rule

102 views1 pages
Published on 18 Nov 2019
School
UC-Davis
Department
Mathematics
Course
MAT 16A
Professor
MaUi
1GA
Kouba
Derive
the
Quotient
Rule
Using
the
Limit
definition
of
the
Derivative
Let
F(x)
=
It’s
derivative
is
g(x)
F’(x)
=
lim
F(x
+
Ii)
F(x)
ii
f(x—h)
=
im
g(z)
h—C
Ii
=
urn
f(x
+
h)g(x)
f(x)g(x
±
1
gfr+h)g(x)
Ii
=
urn
f(x
+
k)g(x)
f(x)g(x) +f(x)g(x)
f(x)g(z
+
Ii)
1
h-*o
g(x+h)g(x)
Ii
-
urn
g(x)(f(x
+
h)
-
f(x))
-
f(x)(g(x
+
h)
-
h-tO
g(x+h)g(x)
k
km
@)
f(r+h)—f(x)
f(x)
g(x-,-h)—g(x)
h—0
g(x-h)g(x)
-
g(x)f’(x)
-
f(x)g’(x)
[g(z)j2
i.e.,
D’
f(x)
j
g(x)f’(x)
f(x)g’(x)
g(x)J
[g(x)]2
1
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