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Help with this derivative.

  1. Mar 22, 2013 #1
    1. The problem statement, all variables and given/known data
    I'm working on implicit differentiation and there is one part of the problem i'm having trouble with so I just pulled it out.
    d/dx[6+sin(xy)]


    2. Relevant equations



    3. The attempt at a solution
    They get the answer of this to be sin(xy) [(x) dy/dx+y] How do they get that? Here is what I get and how I arrive at it.
    d/dx[6+sin(xy)]= d/dx[sin(xy)]= cos(xy) [d/dy (xy) ][dy/dx]= xcos(xy)dy/dx I believe the x comes out because we are evaluating the derivative of y at x, so the y is one but the x comes out, is that the right idea? Thanks.

    -Kevin
     
  2. jcsd
  3. Mar 22, 2013 #2

    Fredrik

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    Are you sure its sin, and not cos?

    Where did the d/dy come from? I guess you must have rewritten d/dx as dy/dx d/dy, using the chain rule. That seems unnecessary, since it's not easier to apply d/dy to xy than to apply d/dx to it.
     
  4. Mar 22, 2013 #3
    Yes sorry it is cos(xy)
    Yes, I was using the chain rule. So if apply d/dx to it then the answer for that part would be y correct?
     
  5. Mar 22, 2013 #4

    SammyS

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    You should have

    [itex]\displaystyle \frac{d}{dx}(\sin(xy))=\cos(xy)\frac{d}{dx}(xy)\ .[/itex]

    Now, what is [itex]\displaystyle \ \ \frac{d}{dx}(xy)\ ?[/itex]
     
  6. Mar 23, 2013 #5
    Upon working through the problem again from the start I was able to solve it. I guess I was just tired when I first attempted it. Thanks for the help!
     
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