Genady Posted January 19 Share Posted January 19 A cool little example of common confusion with partial derivatives, from Penrose's "The Road to Reality" (he attributes the words in the title to Nick Woodhouse.) Let's consider a function of two coordinates, f(x,y), and a coordinate change X = x, Y = y + x Because the X coordinate didn't change and is the same as the x coordinate, one could expect that the corresponding partial derivatives are the same, f_{X}=f_{x}. And, because the Y coordinate is different from the y, these partial derivatives, f_{Y} and f_{y}, could be expected to differ. In fact, this is just opposite: f_{X}=f_{x}-f_{y} f_{Y}=f_{y} The confusion is caused by the notation: f_{X} does not mean a derivative along X, but rather a derivative with a constant Y; and f_{Y} is not a derivative along Y, but a derivative with a constant X. Link to comment Share on other sites More sharing options...

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