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  "body": "\n## Summary\n\nLet $U \\subseteq \\mathbb{R}^n$ be open. The Jacobian matrix of a map $f \\colon U \\to \\mathbb{R}^m$ at a point $a$ is the $m \\times n$ matrix of all first [[partial derivatives|09EGC6F8PT]] $\\partial f_i / \\partial x_j$ at $a$.\nWhen $f$ is differentiable at $a$, it is the matrix of the [[total derivative|0FNKFT8H6E]] $Df(a)$ in the standard bases.\n",
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