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Differentiate the function,ln

Petrus

Well-known member
Feb 21, 2013
739
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 im doing right.
 

Amer

Active member
Mar 1, 2012
275
correct
 

Opalg

MHB Oldtimer
Staff member
Feb 7, 2012
2,706
It's correct as far as it goes, but you could certainly simplify it a bit.
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
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).