What is the Derivative of cos(sin(x)) and Why is it Different from -sin(sin(x))?

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Homework Help Overview

The discussion revolves around the differentiation of the function cos(sin(x)) and the confusion regarding its derivative compared to -sin(sin(x)). The subject area is calculus, specifically focusing on the application of the chain rule in differentiation.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to understand the application of the chain rule and why the derivative of cos(sin(x)) is perceived differently than expected. Some participants clarify the differentiation process and the specific function being discussed.

Discussion Status

The discussion has seen some clarification regarding the differentiation of the function, with participants addressing the original poster's confusion. There is recognition of a mix-up regarding the functions being differentiated, but no explicit consensus has been reached on the derivative itself.

Contextual Notes

Participants are navigating through a misunderstanding related to the specific functions involved in differentiation, with references to previous threads that may not be accessible. The original poster's confusion stems from a misattribution of the differentiation process to a different function.

monet A
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Hi I'm new here, great forum!
On another thread that I can't find I found a message from jamesrc about differentiating cos of sinx that says:

df(g(x))/dx = df(g)/dg * dg(x)/dx by the chain rule, this part I get and I thank james for the help the thing that confuses me is why df(g)/dg = cos(cosx).
Aren't we differentiating df(g) wrt (g) which would give -sin(sinx). What am I missing?
 
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You're not missing anything; you are correct: [itex]d/dx [\cos (\sin x)] = - \sin (\sin x) \cos x[/itex]
 
Oh thanks Al! :smile:
I just found the thread I read and realized that james was differentiating sin of cos not cos of sin, lol.

:blushing:
 
I'm glad you cleared jamesrc's good name! :smile:

And welcome to PF, by the way.
 

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