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  "body": "\n## Definition\n\nLet $I$ be an open interval and let $f \\colon I \\to \\mathbb{R}$ be a function.\nThe function $f$ is differentiable at $a \\in I$ if $f$ has a [[derivative|0F1WR9C83K]] at $a$.\nIt is differentiable on $I$ if it is differentiable at each point of $I$.\n\n## Remarks\n\n[[Differentiable functions are continuous|07ZMX4ANJS]].\nThe converse fails: the [[absolute value|0CQ9ZM383N]] is continuous but not differentiable at $0$.\nPolynomials, the exponential function, and the sine are differentiable on $\\mathbb{R}$.\nMathlib defines differentiability at a point as `DifferentiableAt`.\n\n## Explanations\n\n### L1 human\n\nA differentiable function has a well defined slope at each point.\nIts graph is smooth, with no corners and no vertical tangents.\n",
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