How do you differentiate #f(x)=ln(x/(x-1))#?

1 Answer
Dec 4, 2015

#f'(x) = 1/x - 1/(x-1)#

Explanation:

The easiest way is to use the following logarithmic rule first:

#ln(a/b) = ln(a) - ln(b)#

In your case, it means that

#f(x) = ln(x/(x-1)) = ln(x) - ln(x-1)#

Now, with the knowledge that #(ln x)' = 1/x#, you can differentiate your function as follows:

#f'(x) = 1/x - 1/(x-1)#