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  "body": "\n## Definition\n\nLet $I$ be an open interval, let $f \\colon I \\to \\mathbb{R}$ be a function, and let $a \\in I$.\nA real number $L$ is the derivative of $f$ at $a$ if\n$$\\lim_{h \\to 0} \\frac{f(a + h) - f(a)}{h} = L.$$\nThe notation is $f'(a) = L$.\n\n## Remarks\n\nThe quotient is the slope of the line through $(a, f(a))$ and $(a + h, f(a + h))$. The limit is a [[limit of a function|0TXTSEMHR5]] of $h$ at $0$.\nThe derivative is unique when it exists.\nFor example, the derivative of $x^2$ at $a$ is $\\lim_{h \\to 0} (2a + h) = 2a$.\nMathlib defines the relation \"$f$ has derivative $L$ at $a$\" as `HasDerivAt`.\n\n## Explanations\n\n### L1 human\n\nThe derivative of $f$ at $a$ is the instantaneous rate of change of $f$ at $a$.\nGeometrically, it gives the steepness of the graph at the point $(a, f(a))$.\n",
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