math
wenwen123
Lesson5-DerivativesbyDefinition.docxNAME: ________________________________________________________________________
Derivative by definition:
Some textbooks may define the definition in terms of delta x denoted as in the following:
First, use the definition of the limit to differentiate the following function. Second, use the power rule or derivative of the trig function rules to differentiate the given function below and compare the two derivative answers to see if they match.
1. 2.
2
()25
:'()45
fxyxx
ansfxx
==+
=+
2
7
:'21
yxx
ansyx
=-+
=-
2
3.3
:'6
yx
ansyx
=
=
4.53
:'5
yx
ansy
=+
=
1
21
5.()21
:'()
x
fxx
ansfx
+
=+
=
(
)
(
)
2
1
1
6.
'
x
x
x
y
x
y
=
=-
(
)
(
)
(
)
(
)
(
)
(
)
'
'
0
lim
x
xhx
xx
x
h
df
ff
fsameasf
dxh
+
®
éù
-
ëû
éù
=®=
ëû
x
D
(
)
(
)
(
)
(
)
(
)
(
)
'
'
0
lim
x
xxx
xx
x
x
df
ff
ff
dxx
+D
D®
éù
-
ëû
éù
===
ëû
D
