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How to get the nth order derivative of y=cos3x*cos2x

How to get the nth order derivative of y=cos3x*cos2x

Grade:12th pass

2 Answers

Saurabh Koranglekar
askIITians Faculty 10341 Points
one year ago
Arun
25763 Points
one year ago
 
Dear Rishika
 
cos x cos 2x cos 3x = cos 2x [ cos 4x + cos 2x ] /2 
=(1/2)[ cos 4x cos 2x + cos^2 2x] 
=(1/4) [cos 6x + cos 2x + ( 1 + cos 4x)] 
= (1/4) [ 1 + cos 2x + cos 4x + cos 6x ] 
Now we have D^n ( cos (ax + b) = a^n cos ( n pi/2 + ax + b). 
Thus, D^n( cos x cos 2x cos 3x ) = D^n [ (1/4) { 1 + cos 2x + cos 4x + cos 6x}] 
= (1/4) [ 2^n cos(n pi/2 + 2x) + 4^n cos ( n pi/2 + 4x) + 6^n cos( n pi/2 + 6x) ]

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