Question

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

Answer 1

`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)`