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Implicit differentiation

  1. Apr 21, 2010 #1
    1. The problem statement, all variables and given/known data

    If [tex] y= \ln \sqrt{xy}[/tex] , find the value of dy/dx when y=1

    2. Relevant equations

    3. The attempt at a solution

    [tex] \frac{dy}{dx} = \frac{1}{\sqrt{xy}} \cdot \frac{1}{2\sqrt{xy}}\cdot (x\frac{dy}{dx}+y)[/tex]

    [tex]\frac{dy}{dx}=\frac{1}{x}[/tex] , when y=1
  2. jcsd
  3. Apr 21, 2010 #2


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    Looks correct so far.
    Did you try plugging in y = 1 and simplifying?
  4. Apr 21, 2010 #3


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    You answer should be a number, not a function of x. Since y= ln(xy), when y= 1, 1= ln(x). What is x?
  5. Apr 21, 2010 #4
    this kept me wondering again , if i differentiate first , then plug y=1 in , i get dy/dx=1/x

    and now , if i plug y=1 in first , and differentiate later ,

    1= ln sqrt(x)


    Are they supposed to end up with the same result ?
  6. Apr 21, 2010 #5


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    In all such problems, you have to differentiate first, then substitute the values.
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