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Implicit Differentiation

  1. Feb 14, 2015 #1
    I unfortunately keep on getting the wrong answer to this problem.

    I am supposed to find: dw/dy(1/(w^2+x^2)+1/(w^2+y^2))

    I attached a picture of how I tried to solve it. Help would be much appreciated.
     

    Attached Files:

  2. jcsd
  3. Feb 14, 2015 #2

    Mark44

    Staff: Mentor

    No. What you wrote above doesn't mean what you think.
    I believe what you are supposed to do is use implicit differentiation to find ##\frac{\partial w}{\partial y}##, although that is not clear from what you wrote on the first line. On the third line you have a mistake. Since ##\frac{1}{w^2 + x^2}## does not involve y, its partial derivative with respect to y is zero.
     
  4. Feb 14, 2015 #3

    RUber

    User Avatar
    Homework Helper

    That 2y should also be part of the multiplication. Double check your application of the chain rule on (w^2+y^2).
     
  5. Feb 14, 2015 #4

    SammyS

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    Staff Emeritus
    Science Advisor
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    Gold Member

    You mean that you need to find ∂w/∂y given that (1/(w2+x2)+1/(w2+y2)) = 1. Right ?

    Hello Sebastian B. Welcome to PF !

    In your third equation, you need to have parentheses around ##\displaystyle \ \left( 2w\frac{\partial w}{\partial y}+2y \right) \ ## .

    After that the algebra is messed up.

    Don't forget; the right side of the equation is zero at that point.
     
  6. Feb 14, 2015 #5
    Mark 44: Thank you for your feedback. I realised that I wasn't clear enough with stating my problem, but you figured out what I meant. However,
    \[\delta\]w/\[\delta\]y (w^2+x^2) does not equal zero, because w could be dependent on y
     
  7. Feb 14, 2015 #6
    Ruber and Sammys thanks a lot for the feedback, it helped a lot! I finally figured it out and got the correct answer thanks to you guys. What a dumb error that was. Thanks again!
     
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