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

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SUMMARY

The derivative of the function $\frac{1+\ln(t)}{1-\ln(t)}$ is correctly calculated as $\frac{1/t(1-\ln(t))-(-1/t)(1+\ln(t))}{(1-\ln(t))^2}$. However, further simplification is recommended to enhance clarity and elegance. Simplifying derivatives is essential for improving algebra skills and is crucial for identifying critical numbers and optimizing functions.

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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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