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| PAGE: 139 | SET: Exercises | PROBLEM: 113 |
(a) Find the first, second, third and fourth order derivatives of the function.
The function is 
, where 
is a constant.
Apply derivative on each side with respect to 
.
The first derivative is 
.
Again apply derivative on each side with respect to 
.
The second derivative is 
.
Again apply derivative on each side with respect to .
The third derivative is 
.
Again apply derivative on each side with respect to .
The fourth derivative is 
.
(b)
The second derivative is .
Substitute 
.
.
(c)
The first derivative is .
The second derivative is .
The third derivative is .
The fourth derivative is 
.
Observe the odd derivatives 
and 
.
General rule for odd order deivatives 
.
Observe the odd derivatives 
and 
.
General rule for even order deivatives 
.
(a)
The first derivative is .
The second derivative is .
The third derivative is .
The fourth derivative is .
(b) 
.
(c)
General rule for even order deivatives 
.
General rule for odd order deivatives 
.
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