1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Use logarithmic differentiation to find the derivative

  1. Dec 13, 2012 #1
    Hi ..


    Use logarithmic differentiation to find the derivative

    647224042.jpg

    can please check my answer and How I can know if the question want answer by using logarithmic differentiation or not ?
     
  2. jcsd
  3. Dec 14, 2012 #2

    Mark44

    Staff: Mentor

    In your 4th line you have a mistake.
    Your 3rd line is:
    ln y = (1/2) ln(x2 + x)

    When you differentiate the left side, you should get (1/y) y', due to the chain rule.

    In your last line a factor of y seems to have magically popped up on the right side. You got the right value for the derivative, but several steps in between are incorrect.
     
  4. Dec 14, 2012 #3

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Answer is correct, but as Mark pointed out there are some errors along the way.

    It could be simplified. You have [itex]\ \sqrt{x^2+x}\ [/itex] in the numerator and x2 + x in the denominator.

    If you have x in an exponent and also have x in the base, then logarithmic differentiation can be helpful.

    The function you are differentiating here can be done more easily by simply applying the chain rule.
     
  5. Dec 14, 2012 #4
    You usually use logarithmic differentiation when the exponent is also a variable.

    BiP
     
  6. Dec 14, 2012 #5
    thanks so much ...
     
  7. Dec 14, 2012 #6
    can check this answer please

    828239533.jpg
     
  8. Dec 14, 2012 #7

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    You really should start a new thread for this.

    The 1/3 multiplies both logarithms .
     
  9. Dec 14, 2012 #8
    thansk
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook