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Partial Derivative

  1. Jan 19, 2012 #1
    let f(x, y') = x + y'
    where y' = dy/dx
    then is it true, and why, that the partial derivative of f with respect to y' = 1
    in this case we consder dx/dy' = 0, as if they are independent of each other.
     
  2. jcsd
  3. Jan 19, 2012 #2
  4. Jan 19, 2012 #3
    but since y' = dy/dx , then y depends on x, and y' might depend on x too
    therefore there might be a relation between x and y', and dx/dy' doesn't necessarily equal zero
     
  5. Jan 19, 2012 #4
    To tell the truth, that bothered me as well when I first encountered the concept. The professor was confused as to why I even asked the question. Consider a function f(x,y). Is there any problem with defining partial derivatives with respect to x and y? What if, unbeknownst to you, y is actually a function of x? Well, the answer is no problem. As far as f(x,y) is concerned, y is just a parameter that can take any value. You can substitute the relationship y(x) into the mix after you take the partial derivative.
     
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