How may I derive this equation?

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Homework Help Overview

The original poster seeks to derive the equation y=cos^3(sinx), specifically looking for the derivative of the function.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of the chain rule in differentiation, with some suggesting multiple applications of it. There is also a clarification on the terminology used, specifically whether "derive" refers to differentiation.

Discussion Status

Participants are exploring various approaches to differentiate the function, with some providing guidance on the chain rule. The discussion includes attempts to clarify the original question and confirm understanding of differentiation concepts.

Contextual Notes

There is some confusion regarding the exact nature of the problem, particularly in terms of terminology and the application of differentiation rules. The original poster indicates a need for clarification on the steps involved in the derivation process.

staka
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How may I derive y=cos^3(sinx)?
I thought simply just y=3cos(sinx)^2(cosx)...

Answer given is -3cosxsin(sinx)cos^2(sinx) but no idea how to get to that.
 
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I am a bit confused about what the exact question is. What is it?
 
How to derive the function: y=cos^3(sinx) is my question... solving for y'=.
 
I think you didn't use the chain rule enough times.
You need the derivative of cos3(sin(x)) with respect to cos(sin(x)) times the derivative of cos(sin(x)) wrt sin(x) times the derivative of sin(x) wrt x.
 
By derive you mean differentiate, right?

Try writing t=sinx, then y=[cos(t)]^3. Then, dy/dx=(dy/dt)(dt/dx). Course, you need to use the chain rule again when differentiating y wrt t.
 
Alright. I'll retry.. solving.
 
Oh, differentiate now I know what you are trying to do. Are you familiar with the chain rule?
 
I am familar with the chain rule.. I'll retry.
 
Alright thanks. I've solved it correctly.
 

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