1. Not finding help here? Sign up for a free 30min 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!

Complicated derivative question

  1. Feb 18, 2014 #1
    1. The problem statement, all variables and given/known data

    How to I find the derivative of
    ##y=\sqrt{\sqrt{(1+\sqrt{x})}-1}##

    2. Relevant equations
    Logarithmic derivative


    3. The attempt at a solution
    I decided to take natural logs to both sides, and this is what I have:
    ##\ln y=\frac{1}{2} \ln (\sqrt{(1+\sqrt{x})}-\frac{1}{2}##
    ##\ln y=\frac{1}{4} \ln(1+\sqrt{x})-\frac{1}{2}##
    Then an implicit derivative gave me this:
    ##\frac{1}{y} \frac{dy}{dx}=\frac{1}{8} (\frac{1}{\sqrt{x}+x})##

    Now when I multiply both sides by y, the expression becomes very complicated. How do I manipulate them? :(
     
  2. jcsd
  3. Feb 18, 2014 #2

    maajdl

    User Avatar
    Gold Member

    Why would you want to simplify the expression?
    Just leave it as it is.
     
  4. Feb 18, 2014 #3
    The reason is I need to find dy/dx in terms of x. :(
     
  5. Feb 18, 2014 #4

    maajdl

    User Avatar
    Gold Member

    Then substitute the expression for y, and that's it.
     
  6. Feb 18, 2014 #5
  7. Feb 18, 2014 #6
    Chain rule seems complicated... :(
     
  8. Feb 18, 2014 #7

    DrClaude

    User Avatar

    Staff: Mentor

    You made a mistake there.
    ##\ln y=\frac{1}{2} \ln ( \sqrt{(1+\sqrt{x})}-1)##
     
  9. Feb 18, 2014 #8
    Wasn't it looks the same when expanded?
     
  10. Feb 18, 2014 #9

    DrClaude

    User Avatar

    Staff: Mentor

    When expanding what? ##\ln(a+b) \neq \ln(a) + \ln(b)##
     
  11. Feb 18, 2014 #10
    Oops, my bad. :P
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted