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!

Homework Help: Natural logarithmic function

  1. Feb 24, 2008 #1
    Find y' if y= ln( x^2 + y^2)

    I thought this was just a regular natural log derivative combined with the chain rule.
    So what I got was (2x + 2y)/ (x^2 + y^2)

    But this wasn't the correct answer. So could someone help point out my mistake.
    Thank you.
  2. jcsd
  3. Feb 24, 2008 #2


    User Avatar

    This is implicit differentiation. Since you have y = f(x,y) instead of y = f(x), you have to assume y does equal to some function of x then take derivatives on both sides and solve for y'. Since we made the assumption y can be written as some function of x, D(y^2) = 2yy'. Now, you have to solve for y' just in terms of x and y to get the final answer.

    Forgot to mention y' can be in terms of x AND y since we don't know what y is there's no way to remove it from the expression without solving for y in the original equation which is what we were trying to avoid in the first place.
    Last edited: Feb 24, 2008
  4. Feb 24, 2008 #3
    Oh okay thank you
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook