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Homework Help: What is the derivative of y=sin(x+y)?

  1. Oct 12, 2005 #1
    what is the derivative of y=sin(x+y)???

    what is the derivative of y=sin(x+y)???
     
  2. jcsd
  3. Oct 12, 2005 #2
    The partial derivatives of [itex]f(x,y) = sin(x+y)[/itex] are [itex]\frac{df}{dx} = cos(x+y)[/itex] and [itex]\frac{df}{dy} = cos(x+y)[/itex]
     
  4. Oct 12, 2005 #3

    Diane_

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    Homework Helper

    mattsoto - What do you want the derivative with respect to? If it's anything other than x or y, we need to talk a bit more.
     
  5. Oct 12, 2005 #4
    the derivative is respect to y, Diane...
     
  6. Oct 12, 2005 #5

    HallsofIvy

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    The derivative of y, given y= sin(x+ y), with respect to x, using implicit differentiation: y'= cos(x+y)(1+ y') so y'- y'cos(x+y)= cos(x+ y) and
    y'= cos(x+y)/(1- cos(x+y)).

    The derivative of x, given y= sin(x+ y), with respect to y (which is what you told you Diane you want, but I doubt since I would read what you originally wrote as 'the derivative OF y= ...), by implicit differentiation: 1= cos(x+y)(x'+ y) so
    1- ycos(x+y)= cos(x+y)x' and x'= (1- ycos(x+y))/cos(x+y).
     
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