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    Derivative
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Homework Help Overview

The discussion revolves around finding the derivative of the expression 2sin(x)cos(x) without simplifying it. The subject area is calculus, specifically focusing on differentiation and trigonometric identities.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the correctness of the derivative calculated and suggest simplifications. Questions arise about whether the result resembles known trigonometric identities and if the derivative could be approached differently using those identities.

Discussion Status

The discussion includes confirmations of correctness regarding the derivative, along with suggestions for simplification. Participants explore the relationship between the derivative and trigonometric identities, indicating a productive exchange of ideas without reaching a definitive conclusion.

Contextual Notes

Some participants note the importance of simplification in the context of the problem, while others hint at alternative methods involving trigonometric identities. There is no explicit consensus on the necessity of simplification or the preferred approach.

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1 more derivative problem!

Homework Statement


Find the derivative of...
2sinxcosx
not simplified

The Attempt at a Solution


(2cosxcosx) - (2sinxsinx)

I just want to make sure this is right
 
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yes that is correct..but you should simplify cosxcosx to [tex]cos^2x[/tex] and likewise with the sinxsinx
 
rock.freak667 said:
yes that is correct..but you should simplify cosxcosx to [tex]cos^2x[/tex] and likewise with the sinxsinx

And, when you're done, does that result look like a trig identity you've seen before? Could you have gotten the same result by using a trig identity on 2 sin x cos x first?
 


dy/dx = 2 sin x . -sin x +cos x . cos x= 2 ( cos squared - sin squared)

So yes your correct
 
Last edited:


Which, as dynamicsolo hinted, is the same as 2 cos(2x) and could have been done more simply by recognizing that 2 sin(x) cos(x)= sin(2x).
 

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