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Homework Help: Partial Derivative Question

  1. May 16, 2012 #1
    1. The problem statement, all variables and given/known data
    If f(x,y) = x(x^2+y^2)^(-3/2)*e^(sin(x^2y)) find the derivative of f with respect to x at the point (1,0).

    3. The attempt at a solution
    The textbook solution just plugs 0 into y and gets f(x) = x^-2 and then proceeds to differentiate this resulting in the answer -2. I don't understand why this is legal. How can you just plug the point into the function and then take the derivative?

    For example, if I had the function y = x and I wanted the derivative at x=0. You can't just plug in zero and take the derivative...?
  2. jcsd
  3. May 17, 2012 #2


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    Science Advisor
    Homework Helper

    Because when you taking a partial derivative of a function of two variables f(x,y) with respect to x you assume y is a constant. You can either find it for any y or plug in a value for y to being with. y=x isn't a function of two variables.
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