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Total/Partial derivatives

  1. Feb 21, 2012 #1
    Are the following equalities between total and partial derivatives true if [itex]\frac{dy}{dx}=f(x,y)[/itex]? [tex]\displaystyle \frac{df}{dx} = \frac{\partial f}{\partial x} + \frac{\partial f}{\partial y} f(x,y)[/tex] [tex]\displaystyle \frac{d^2f}{dx^2} = \frac{\partial f}{\partial x}\frac{\partial f}{\partial y} + \left( \frac{\partial f}{\partial y} \right) ^2 f(x,y)[/tex]
     
  2. jcsd
  3. Feb 21, 2012 #2
    This is a good resource
    http://en.wikipedia.org/wiki/Total_derivative
     
  4. Feb 21, 2012 #3
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