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The book considers f(x,y) = (x, -y), saying that f is differentiable and that "Its derivative at a point is the linear map given by its Jacobian...". I don't understand, for example, how the derivative is a linear map. I associate (perhaps incorrectly) the derivative with a rate of change. Could someone recommend some resources (books, websites etc) for understanding the differentiation of such functions?

Domhal