Implicit Differentiation - Second Derivative

  1. Were assigned questions regarding implicit differentiation and the second derivative but did not receive a formal lesson so I need some explanations.

    Example:

    Find the second derivative
    x^3 + y^3 = 1

    I found this solution on the internet and the answer matches the one in the textbook.

    [​IMG]

    However, I don't understand how -2xy^3 - 2x^4/y^5 turned into just -2xy^3/y^5 (This is the 5-6 step). Furthermore, I don't see how -2xy^3/y^5 equals -2x(y^3 + x^3)/y^5 (6-7 step).

    Simply, I need explanations for this solutions rationale. Thanks.
     
    Last edited: Apr 1, 2006
  2. jcsd
  3. nrqed

    nrqed 3,048
    Science Advisor
    Homework Helper

    There is an obvious typo in step 5-6...the -2x^4/y^5 term disappears and then reappears on the next line .

    At the very end they use x^3+y^3=1, which was the initial equation.
     
  4. Ahhh, now I see it, thanks for pointing that out!
     
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