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How to differentiate e^(x+y) for x?

  1. Feb 7, 2008 #1
    1. The problem statement, all variables and given/known data

    if f(x,y) is e^(x+y) am i right in saying dy/dx is e^(x+y)


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 7, 2008 #2

    HallsofIvy

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    If y is not a function of x, dy/dx makes no sense at all! (Except for dy/dx= 0.)
    The notation f(x,y)= ex+y implies that x and y are independent variables. Without further information, you can find [itex]\partial f/\partial x[/itex] or [itex]\partial f/\partial y[/itex] but not dy/dx.

    If, for example, you know that f(x,y)= ex+y= constant, then you can use "implicit differentiation": (1+ dy/dx)ex+y= 0 and determine that dy/dx= -1.
     
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