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

[Petrus]

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.

 

[Amer]

correct

 

[Opalg]

It's correct as far as it goes, but you could certainly simplify it a bit.

 

[MarkFL]

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).