How to Find the Derivative of f(x)=ln[x/(x-1)]?

[lreichardt]

How do I take the derivative of

f(x)=ln[x/(x-1)]?

Thanks!

 

[tiny-tim]

Welcome to PF!

Hi lreichardt! Welcome to PF!

Just use the chain rule: derivative of ln, times the derivative of x/(x-1).

 

[lreichardt]

so, (x/1)(quotient rule of x/(x-1)? =

(x/1)(-x/x-1)=-x^2/x-1

 

[tiny-tim]

ooh dear …

better go the easy way … simplify it first …

ln(x/(x-1)) = ln(x) - ln(x-1) … now differentiate!

 

[kelten]

Chain rule = The difference of the derivative of the "Outer" and derivative of the "Inner", put simply.

 

[lreichardt]

Thanks all, figured it out.