How to Simplify the Derivative of $\frac{1+\ln(t)}{1-\ln(t)}$?

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Discussion Overview

The discussion focuses on the differentiation of the function $\frac{1+\ln(t)}{1-\ln(t)}$. Participants explore the correctness of the derivative and the potential for simplification of the result.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant presents the derivative as $\frac{1/t(1-\ln(t))-(-1/t)(1+\ln(t))}{(1-\ln(t))^2}$ and seeks confirmation of its correctness.
  • Another participant confirms that the differentiation is correct.
  • Some participants suggest that while the derivative is correct, it could be simplified further.
  • There is an emphasis on the importance of simplification for improving algebra skills and for practical applications such as finding critical numbers and optimization.

Areas of Agreement / Disagreement

Participants generally agree on the correctness of the derivative, but there is no consensus on the extent or method of simplification.

Contextual Notes

No specific limitations or unresolved mathematical steps are noted in the discussion.

Who May Find This Useful

Individuals interested in calculus, particularly in differentiation techniques and simplification of expressions.

Petrus
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Differentiate the function: $\frac{1+\ln(t)}{1-\ln(t)}$
Is this correct?
$\frac{1/t(1-\ln(t))-(-1/t)(1+\ln(t))}{(1-\ln(t))^2}$
I got none facit in My textbook so I would like to someone confirmed I am doing right.
 
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correct
 
It's correct as far as it goes, but you could certainly simplify it a bit.
 
Opalg said:
It's correct as far as it goes, but you could certainly simplify it a bit.

Yes, this is a good habit to get into, as not only does it improve your algebra skills and just looks more elegant to express results in a simpler more compact form, it is also crucial for finding critical numbers when you are looking at the behavior of the original function or for optimization (finding extrema).
 

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