Differentiation Rules of Sinusoidal Functions

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Homework Help Overview

The discussion revolves around the differentiation of the function f(x) = cos(2x) - sin(2x). Participants are attempting to find the derivative and are comparing their results with a provided answer from a textbook.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are discussing the differentiation process and questioning the correctness of their calculations. There is an exploration of potential simplifications and identities related to sine and cosine functions.

Discussion Status

Some participants have identified a discrepancy between their results and the textbook answer. Guidance has been offered regarding trigonometric identities that may clarify the situation. The discussion is ongoing, with participants reflecting on their mistakes and seeking further understanding.

Contextual Notes

There is an indication that the original poster may have overlooked a trigonometric identity relevant to the differentiation process. The discussion includes a focus on the implications of this oversight.

chudzoik
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Homework Statement


f(x) = cos2x - sin2x

The Attempt at a Solution


f'(x) = (2cosx)(-sinx) - (2sinx)(cosx)
f'(x) = -2cosxsinx - 2sinxcosx

This is what I think the answer should be, but the back of the book says otherwise. I need help identifying what I did wrong.
 
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chudzoik said:

Homework Statement


f(x) = cos2x - sin2x

The Attempt at a Solution


f'(x) = (2cosx)(-sinx) - (2sinx)(cosx)
f'(x) = -2cosxsinx - 2sinxcosx

This is what I think the answer should be, but the back of the book says otherwise. I need help identifying what I did wrong.
... And what would that otherwise be?

Perhaps something involving sine and/or cosine of 2x ?

... or just a simplified version of what you have?

-2ab - 2ba = -4ab ?
 
SammyS said:
... And what would that otherwise be?

Perhaps something involving sine and/or cosine of 2x ?

... or just a simplified version of what you have?

-2ab - 2ba = -4ab ?

It says the answer should be f'(x) = -2sin2x.
 
chudzoik said:
It says the answer should be f'(x) = -2sin2x.

Recall this identity: 2sin(x)cos(x) = sin(2x)
 
Oh wow forgot entirely about that. These kinds of mistakes will be the end of me. :redface: Thanks for the help.
 

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