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Using implicit differentiation: Is this correct?

  1. Oct 16, 2012 #1
    1. The problem statement, all variables and given/known data

    I need to use implicit differentiation to find the derivative of y=sin(x+y).

    2. Relevant equations



    3. The attempt at a solution

    This is what I did:

    y=sin(x+y)
    y'=(sin(x+y))'
    y'=(1+y')(cos(x+y)) (by the chain rule)

    Now, what do I do? Is this correct:

    y'=cos(x+y)+cos(x+y)y'
    y'-cos(x+y)y'=cos(x+y)
    y'(1-cos(x+y))=cos(x+y)
    y'= cos(x+y) / 1-cos(x+y)

    ?
     
  2. jcsd
  3. Oct 16, 2012 #2

    SammyS

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    It's correct with the added parentheses.
     
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