Derivative of Cos^3(x)*Sin(x) using Chain Rule

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Homework Help Overview

The discussion revolves around finding the derivative of the function \( \cos^3(x) \cdot \sin(x) \) using the chain rule and product rule in calculus.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of the product rule and chain rule, with some attempting to clarify the function's structure. There are questions about the correctness of the derivative calculations and the need for a complete answer.

Discussion Status

Some participants have offered guidance on the rules to apply, while others are exploring the correctness of the derivative steps presented. There is no explicit consensus on the final answer, but the discussion is actively engaging with the problem.

Contextual Notes

There is mention of Physics Forums' policy against providing complete answers, which influences the nature of the responses and guidance offered.

CloDawg
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Help!
I last did this kind of work years ago in university. Can som1 please help me with the derivative.
 
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I think the question is ((cosx)^3)*sin(x).Am I right?The formula for d(uv)/dx=u(dv/dx)+v(du/dx).And of course I think you need only formula.Do you need answer?
 
omkar13 said:
I think the question is ((cosx)^3)*sin(x).Am I right?The formula for d(uv)/dx=u(dv/dx)+v(du/dx).And of course I think you need only formula.Do you need answer?
It is against Physics Forums policy to provide answers to posters' questions.
 
Thats it chain rule or something:


d(uv)/dx=u(dv/dx)+v(du/dx)

u=sin(x)
v=cos^3(x)

(dv/dx) = -3sin((x))cos^2(x)
(du/dx) = cos(x)

d(uv)/dx= -3sin^2(x)cos^2(x) + cos^4(x)

Is this correct?
 

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