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Implicit Differentiation Question

  1. Nov 6, 2016 #1
    1. The problem statement, all variables and given/known data
    I am told to find dy/dx by implicit differentiation where:
    e^(x^2 * y) = x + y

    2. Relevant equations
    The above equation and the ln of it.


    3. The attempt at a solution
    e^(x^2 * y) = x + y
    (x^2 * y)ln(e) = ln(x+y)
    x^2 * y = ln(x+y)
    x^2(dy/dx) + y(2x) = 1/(x+y) * (1 + dy/dx)
    (dy/dx)[x^2 - 1/(x+y)] = 1/(x+y) - 2xy
    dy/dx = (1/(x+y) - 2xy)/(x^2 - 1/(x+y))

    or here: https://postimg.org/image/3k5ygbkxt/

    This was marked wrong (online software). It doesn't care about simplest form and it was entered properly. So, what did I do wrong?
     

    Attached Files:

  2. jcsd
  3. Nov 6, 2016 #2

    fresh_42

    Staff: Mentor

    I got the same result without using the logarithm, only with a single quotient, i.e. expanded by ##x+y##. Maybe the missing brackets in your linear notation led to the online error. Or it is expected to write ##e^{x^2y}## instead of ##x+y## in the solution.
     
  4. Nov 6, 2016 #3
    I just put it in replacing x+y with e^(x^2 * y) and it worked. Thanks!
     
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