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  "body": "\n## Statement\n\nLet $f$ and $g$ be real functions on an open interval $I$, both differentiable at $a \\in I$, with $g(a) \\ne 0$.\nThen $f/g$ is differentiable at $a$, and\n$$\\left( \\frac{f}{g} \\right)'(a) = \\frac{f'(a) g(a) - f(a) g'(a)}{g(a)^2}.$$\n\n## Remarks\n\nWrite $f/g = f \\cdot (1/g)$, and use the [[product rule|0V9A43H7WV]] and the [[reciprocal rule|0QD4E5JYPT]].\nFor example, it gives $(\\tan x)' = 1/\\cos^2 x$.\nMathlib states it as `HasDerivAt.div`.\n\n## Explanations\n\n### L1 human\n\nThe rule gives the slope of a quotient from the values and slopes of the numerator and the denominator.\nA common memory aid is \"low d-high minus high d-low, over low squared\".\n",
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