Help with Derivatives of Cubic Root Function

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Homework Help Overview

The original poster seeks assistance in finding the derivatives of the cubic root function defined as the cubic root of the expression \((x^3+1)/(x^3-1)\).

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relevance of the chain rule and quotient rule in the context of the problem. There are inquiries about how to handle the cubic root and its conversion to exponent form, as well as questions regarding the derivative of simpler root functions.

Discussion Status

Participants are exploring different aspects of differentiation techniques and expressing uncertainty about the manipulation of the cubic root. Some guidance has been offered regarding foundational concepts, but no consensus has been reached on a specific approach.

Contextual Notes

There appears to be some confusion regarding the manipulation of the cubic root and its derivative, which may be affecting the original poster's understanding of the problem.

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Homework Statement



FIND THE DERIVATIVES OF THE FOLLOWING FUNCTION:

CUBEROOT OF ((x^3+1)/(x^3-1))


Homework Equations





The Attempt at a Solution

 
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Well do you know what the chain rule is? quotient rule?

those will probably be pretty useful here.
 
yeah but how do you get rid of the cuberoot
 
Do you know how to take the derivative of Cuberoot(x)?

or how about cuberoot(x^2)

if not those, how about the square root (x)
 
How do you re-write the cuberoot in exponent form? I think that's what's messing you up.
 

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