[SOLVED] Derivatives of cos and sin (again)

May 2010
8
0
okay so my previous question was answered however i know that:

2cos(x).cos(9x)

has the derivative:

-18cos(x)sin(9x) - 2sin(x)cos(9x)

But will 2[cos1/2(f1-f2)t][cos1/2(f1+f2)t] have the same derivative?
with f1= 10 and f2=8
 

pickslides

MHF Helper
Sep 2008
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I believe it will.
 
May 2010
8
0
hrmmm. that makes it all seem a bit too easy then. i am meant to verify the answer from the first equation with that one. But to me they are basically the same.
 

pickslides

MHF Helper
Sep 2008
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1,625
Melbourne
They are the same. Just find the derivavtive of the second to confirm.
 
May 2010
8
0
so from;
y=2[cos1/2(10-8)x][cos1/2(10+8)x]
= 2[cos1/2(2)x][cos1/2(18)x]
=2cosx.cos(9x)

then differentiate that and it should equal

-18cos(x)sin(9x)-2sin(x)cos(9x)

thats like two extra steps rofl.
 

pickslides

MHF Helper
Sep 2008
5,237
1,625
Melbourne
Exactly (Rofl) . You were using a previous result to help you with another. This will happen a lot in your studies.
 
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