My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Thanks Tree4Thanks
  • 1 Post By greg1313
  • 1 Post By Seventy7
  • 2 Post By topsquark
Reply
 
LinkBack Thread Tools Display Modes
March 18th, 2017, 05:56 PM   #1
Newbie
 
Joined: Nov 2016
From: USA

Posts: 26
Thanks: 1

Quick derivative question

Find the derivative of ln(1/x).

Rewrite as lnx^-1, which equals -lnx, whose derivative answer is -1/x.
-------------------------------------------------------------------------------
Why won't this method produce the same answer for the same problem above?:

ln(1/x) = d/dx[ln1- lnx]; law of logs

= 1/1 - 1/x; since d/dx (ln x) = 1/x, and by that same formula d/dx (ln 1) = 1/1 ?

= 1 - 1/x

= x/x - 1/x; common denominator

=(x-1)/x

Last edited by Seventy7; March 18th, 2017 at 06:04 PM.
Seventy7 is offline  
 
March 18th, 2017, 06:07 PM   #2
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,576
Thanks: 931

Math Focus: Elementary mathematics and beyond
$\ln(1)=0$ it's a constant anyway, so the derivative would be zero (for any number).
Thanks from Seventy7
greg1313 is online now  
March 18th, 2017, 06:13 PM   #3
Newbie
 
Joined: Nov 2016
From: USA

Posts: 26
Thanks: 1

That's right. I got caught up in the formula d/dx lnx = 1/x and forgot that ln 1 evaluates to a constant, whose derivative is zero.

Thanks!
Thanks from greg1313
Seventy7 is offline  
March 18th, 2017, 07:01 PM   #4
Math Team
 
topsquark's Avatar
 
Joined: May 2013
From: The Astral plane

Posts: 1,570
Thanks: 613

Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
Originally Posted by Seventy7 View Post
ln(1/x) = d/dx[ln1- lnx]; law of logs
Pet Peeve Warning!! Danger, Will Robinson! Danger!

The above equation is not correct. ln(1/x) is not equal to d/dx[ln(1) - ln(x)]. Now if you wrote ln(1/x) = ln(1) - ln(x) then you are okay.

This has the appearance of writing thoughts down as you have them. I've seen expressions of the form 2x + 1 = 2x + 1 - 1 = x = -1/2. It's stream of thought but is very sloppy. And if your grader can't figure it out you'll lose points on an exam.

Pet Peeve Over and Out!

-Dan
Thanks from greg1313 and Seventy7
topsquark is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
derivative, question, quick, simple



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Quick question. hyperbola Pre-Calculus 7 February 20th, 2015 03:29 AM
Log question (need help quick) schLoL Algebra 5 April 26th, 2011 03:36 PM
Quick question dabdias Calculus 3 April 8th, 2009 08:44 AM
Quick derivative question funsize999 Calculus 6 March 29th, 2009 08:53 PM
Quick Second Partial Derivative Test Question cmmcnamara Calculus 3 March 19th, 2009 09:21 PM





Copyright © 2017 My Math Forum. All rights reserved.