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  "body": "\n## Statement\n\nLet $f$ be a real function on an open interval $I$, differentiable at $a \\in I$, and let $c$ be a real number.\nThen $c f$ is differentiable at $a$, and $(c f)'(a) = c f'(a)$.\n\n## Remarks\n\nIt is the case $\\beta = 0$ of the [[linearity of differentiation|0M0TKFRX2A]].\nFor example, $(5 x^2)' = 10 x$.\nMathlib states it as `deriv_const_mul`.\n\n## Explanations\n\n### L1 human\n\nStretching a graph vertically by a factor $c$ multiplies all its slopes by $c$.\n",
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