Thread: [SOLVED] Derivatives of cos and sin (again)

1. [SOLVED] Derivatives of cos and sin (again)

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

2. I believe it will.

3. 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.

4. They are the same. Just find the derivavtive of the second to confirm.

5. 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.

6. Exactly . You were using a previous result to help you with another. This will happen a lot in your studies.