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The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

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holds, with Image(h) small relative to h. The linear map T is the derivative of u at x.

An important special case of this is when m = 1. If f : ImagenImage is differentiable at x, then the derivative of f at x is a linear map from Imagen to Image. The matrix of T is a row vector ...

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