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This is just a quick check: Is the derivative of the function $f(\vec{x})=\vec{x}$ equal to $1$ or the identity matrix? (I know that this question is quite stupid, but I want to get my definitions right...) Thank you.

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If "derivative" means "Jacobi matrix", then it is the identity matrix.

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    @Pete: You might want to study [this wikipedia article](http://en.wikipedia.org/wiki/Derivative#Derivatives_in_higher_dimensions).2011-11-22