How do I find the Derivative for the Function.


Thanks.

The derivative of ln(x) is 1/x. I'm not sure what you're trying to get at with your formula:


\ln(x) = - \frac 1 {x-1}


This formula is incorrect, so please clarify your question.

hi. I know that the derivative of ln(x) is 1/x. but the original question was to prove that the Function ln(x)=1/x-1 has exactly 2 Solutions

I need to find the derivative.


hope is more clear now :)

You can use the Intermediate Value Theorem and/or Rolles Theorem to prove it has two solutions.

Would like to help you but have not a slightest idea what you want to do here.

Equations ln(x) = 1/x-1 and ln(x) = -1/(x-1) are not the same, so it gets more and more confusing.

The first equation has only one solution, the second -- none.

You can rewrite it as:

ln(x)+\frac{1}{x-1} and then try to show this has exactly two solutions.

The thing is, it does not have two solutions.

But, if it were ln(x)=\frac{1}{x-1}\Rightarrow ln(x)-\frac{1}{x-1}, then it would have the two solutions.

Both graphs appear below.

OK I will try thanks to all of you for helping.