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

Click For Summary

Homework Help Overview

The discussion revolves around finding the derivative of the function f(x) = ln[x/(x-1)], which falls under the subject area of calculus, specifically focusing on differentiation techniques.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of the chain rule and the quotient rule in finding the derivative. There are attempts to simplify the expression before differentiation, with some suggesting using properties of logarithms.

Discussion Status

The discussion includes various approaches to the problem, with participants offering different methods and clarifications. While one participant expresses confidence in having figured it out, there is no explicit consensus on a single method being the best approach.

Contextual Notes

Some participants question the complexity of the derivative process and suggest simplifications, indicating a potential lack of clarity in the original function's setup.

lreichardt
Messages
4
Reaction score
0
How do I take the derivative of

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

Thanks!
 
Physics news on Phys.org
Welcome to PF!

Hi lreichardt! Welcome to PF! :smile:

Just use the chain rule: derivative of ln, times the derivative of x/(x-1). :smile:
 
so, (x/1)(quotient rule of x/(x-1)? =

(x/1)(-x/x-1)=-x^2/x-1
 
ooh dear …

better go the easy way … simplify it first …

ln(x/(x-1)) = ln(x) - ln(x-1) … now differentiate! :smile:
 
Chain rule = The difference of the derivative of the "Outer" and derivative of the "Inner", put simply.
 
Thanks all, figured it out.
 

Similar threads

Find f(x,y) given partial derivative and initial condition
  • · Replies 6 ·
Replies
6
Views
2K
Determine for which x the derivative exists of: ##f(x)=\ln|\sin(x)|##
  • · Replies 2 ·
Replies
2
Views
2K
Determine Convergence/Divergence of Sequence: f(x)=ln(x)^2/x
  • · Replies 34 ·
2
Replies
34
Views
4K
Show that the given function is decreasing
  • · Replies 9 ·
Replies
9
Views
2K
Is this a valid explanation of why ln() is unbounded near zero?
  • · Replies 8 ·
Replies
8
Views
2K
Solve the first order linear differential equation
  • · Replies 26 ·
Replies
26
Views
2K
Why Is the Chain Rule Not Used in Differentiating h(x) = 3f(x) + 8g(x)?
  • · Replies 2 ·
Replies
2
Views
2K
If f is undefined at x=a, can f' exist at x=a?
  • · Replies 9 ·
Replies
9
Views
2K
Differentiable function proof given ##f''(c) = 1##
  • · Replies 1 ·
Replies
1
Views
1K
What Are the Inflection Points of a Second Derivative Function?
  • · Replies 7 ·
Replies
7
Views
2K