Question

differentiate ln(1/x^3) from first principles

Asked by: andieje

Hello

I know how to differentiate lnx from first principles but I've got stuck when i tried to do ln(1/x^3)

Please could someone show me how to do it? If you could refer to the reference on this page
http://www.mathcentre.ac.uk/students.php/mathematics/differentiation/first_principles/resources/

This will show you how i learnt how to differentiate ln(x). That's as far as I know.

Many thanks in advance

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Asked On
2009-09-27 at 17:12:02ID24765708
Topic

Math & Science

Participating Experts
2
Points
500
Comments
7

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    Answers

     

    by: uucknaaaPosted on 2009-09-27 at 18:00:12ID: 25436199

    Hi

    This may not be exactly what you need but it's the first instance of something I've looked up on the new Wolfram/Alpha computational knowledge engine.  I'm sure you'd be interested in reviewing:

    http://www.wolframalpha.com/input/?i=differentiate+ln%281%2Fx%5E3%29

    Check it out and let me know if it helps.

     

    by: GwynforWebPosted on 2009-09-27 at 21:26:47ID: 25436732

    If you can do ln(x) from 1st principle then you can do ln(1/x^3) as we have:-

    ln(1/x^3) = ln(1) - ln(x^3)

                = 0 - 3ln(x)

                = -3ln(x)

     

    by: andiejePosted on 2009-09-28 at 03:32:24ID: 25438034

    Hi GywnforWeb

    That isn't what I call differentiating from first principles. Also, that's not how it's done in the link I provided.

    I want to differentiate ln(1/x^3) using the method given in that link

    So i would start off

    f(x + dx) - f(x) / dx

    ln(x+dx)^-3 - ln(x)^-3 /dx

    Then where do i go?

     

    by: andiejePosted on 2009-09-28 at 04:16:09ID: 25438224

    I worked it out

    f(x+dx) - f(x) /dx

    ln(x+dx)^-3 - ln(x) ^-3  /  dx

    -3ln(x+dx) + 3ln(x)     /   dx

    -3/dx  (ln (x + dx) /x)

    -3/dx  (ln (1 + dx/x))

    And then you can replace dx/x with  t and so on as shown in the link provided to end up with -3/x

     

    by: uucknaaaPosted on 2009-09-28 at 05:02:16ID: 25438503

    Hey ..

    Just wanted to make sure you saw the "show steps", in red, on the right of the derivative at the link I gave.  They even show the proper use of the chain rule.

    Hope it helps.

     

    by: andiejePosted on 2009-09-28 at 12:56:53ID: 25442691

    Great link. I've heard of that site actually

    I'm going to give you the points because of the insight i gained from looking at the function

     

    by: uucknaaaPosted on 2009-09-28 at 13:07:53ID: 25442798

    Thanks -- it's been great working with you on this one.

    20120131-EE-VQP-002

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