Complicated derivative problem

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Homework Help Overview

The discussion revolves around taking the derivative of a complex function involving a variable \( u \) and a parameter \( n \). The function includes terms like \( u^{(n+1)} \) and \( (n+1) \ln(u) - 1 \), which suggests a focus on calculus and differentiation techniques.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of the product rule and the treatment of \( n \) as a constant. Questions arise regarding the correctness of the derivative taken and the simplification of terms post-differentiation.

Discussion Status

Some participants have offered guidance on how to approach the differentiation, including the suggestion to factor out constants and apply the product rule. There is an ongoing exploration of the implications of treating \( n \) as a constant and the resulting expressions from differentiation.

Contextual Notes

Participants are navigating the complexities of the derivative while addressing potential simplifications and clarifying the roles of constants and variables in the function.

demonelite123
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d/du [((u(n+1))/(n+1)2) ((n+1) ln(u) - 1)]

how would you take the derivative of this large complicated function?
 
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First, bring out the factor of 1/(n + 1)^2, since it doesn't depend on u. Then use the product rule on u^(n+1)*((n + 1) ln(u) - 1)
 
so would "n" be a constant in this problem? i took the derivative and i got something like this:

(u(n+1)(n+1)(ln u))(n+1)(lnu - 1) + (u(n+1))(n+1)(1/u)

all of that over (n+1)2. is this right?
 
you still need to decrement the power after differentiation. all of this simplifies considerably.
[edit] you shouldn't have two (ln u) terms.
 

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