If $f:\mathbb R^n\times \mathbb R^m \rightarrow \mathbb R$ then how we define derivative of $f$ at $(x,y)\in \mathbb R^n\times \mathbb R^m$? I am assuming that we should consider $f$ as a function from $\mathbb R^{n+m}$ to $\mathbb R$ and use the definition of derivative of function $f:\mathbb R^{n+m}\rightarrow \mathbb R$. Am I right?
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For future reference, enclose math in $, not `. Additionally, your idea sounds perfectly fine to me. – csch2 Jun 15 '20 at 03:07
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1short answer: yes – user251257 Jun 15 '20 at 03:08
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Seems straightforward enough as you suggest. – herb steinberg Jun 15 '20 at 03:18
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In general, if we have $f:A \to B$, the derivative is a function $Df:A \to L(A, B)$, where $L(A,B)$ is the collection of linear functions from $A$ to $B$. – copper.hat Jun 15 '20 at 04:54