On-line Math 21
On-line Math 21
3.1
Trigonometric functions
3.1.1
Derivatives of sin(x) and cos(x) .
Example 1
Find (tanx)
¢
.
Solution
( tan(x))
¢
=
æ
ç
è
sin(x)
cos(x)
ö
÷
ø
¢
, so we use the quotient rule:
=
(sin(x))
¢
cos(x)
-
(cos(x))
¢
sin(x)
cos
2
(x)
=
(cos(x))cos(x)
-
(
-
sin(x))sin(x)
cos
2
(x)
=
cos
2
(x)+sin
2
(x)
cos
2
(x)
=
1
cos
2
(x)
=
sec
2
(x).
So,
( tan(x))
¢
= sec
2
(x).
Copyright (c) 2000 by
David L. Johnson
.
File translated from T
E
X by
T
T
H
, version 2.61.
On 26 Nov 2000, 23:14.