Chapter 3 Section 5
| d | of sinx = cosx | d | of cosx = -sinx |
| dx | dx |
Examples:
1. y = 3x sinx Use product rule:
3x cosx + sinx (3)
y' = 3x cosx + 3 sinx
| 2. y = | sinx Use quotient rule: |
| 1-cosx |
| (1-cosx)(cosx)-(sinx)(0+sinx) | = | cosx-cos2 x - sin2 x |
|
(1-cosx)2 |
(1-cosx)2 |
| tan x = | sin x | sec x = | 1 |
| cos x | cos x | ||
| cot x = | cos x | csc x = | 1 |
| sin x | sin x |
Derivatives:
| d |
tan x = sec2 x |
d |
sec x = secxtanx |
| dx | dx | ||
| d |
cot x = -csc2 x |
d |
csc x = -cscxcotx |
| dx | dx |
Examples: Find
the derivatives:
1. y = x cscx Product Rule: x(-cscxcotx)+
cscx(1)
-xcscxcotx + cscx
y ' = cscx(1-xcotx)
2. y = cosx + x
sinx
-sinx + x(cosx)+sinx(1)
y ' = x cosx
 |
 |