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Differentiation of exp(xy) wrt x

  1. Mar 24, 2007 #1
    Please help

    Differentiate exp(xy) w.r.t x

    Thanks
     
  2. jcsd
  3. Mar 24, 2007 #2
    You need to show your work/attempt.

    And is y a function of x, or are x and y independent variables?
     
  4. Mar 24, 2007 #3
    differentiate implicitly

    exp(xy) = 0

    i thought i would write it out but i dont know how to write the mathmatical symbols on screen
     
  5. Mar 24, 2007 #4
    Okay, then, use a (') to show a derivative. For example, y' will be the derivative of y w.r.t x.

    Do you know how to differentiate the exponential function?
     
  6. Mar 24, 2007 #5
    exp(x)*exp(y)*y'+exp(y)+exp(x)
     
  7. Mar 24, 2007 #6
    It sort of (but not quite) looks like you're differentiating exp(x)exp(y) rather than exp(xy). Those two are not equal.

    What's the derivative of exp(f(x))?
     
  8. Mar 24, 2007 #7
    i dont know i think thats my problem
     
  9. Mar 24, 2007 #8
    i presume f'(x)*exp(f(x))
     
  10. Mar 24, 2007 #9
    That's correct!

    Now substitute f(x) = xy. What do you get?
     
  11. Mar 24, 2007 #10
    ah thanks just forgot this simple derivation
     
  12. Mar 24, 2007 #11

    Mute

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    There is a problem with your implicit equation there: exp(xy) is never zero, it only approaches it asymptotically. (So technically, the surface doesn't exist, so neither does the derivative!)

    But otherwise, you can just do what you did to get a derivative for other surfaces of exp(xy), e.g. exp(xy) = 5, which will produce a surface, and so the derivative will exist and you'd get the same derivative as if you tried to differentiate exp(xy) = 0.
     
  13. Mar 24, 2007 #12
    i didnt give the whole equation because i could take the derivatives of the other functions
    the full equation is x + y + exp(xy) = 0
     
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