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  "body": "\n## Statement\n\nLet $p(x) = \\sum_{k=0}^{n} a_k x^k$ with real coefficients $a_k$.\nThen $p$ is differentiable on $\\mathbb{R}$, and\n$$p'(x) = \\sum_{k=1}^{n} k a_k x^{k-1}.$$\n\n## Remarks\n\nIt follows from the [[power rule|0JZGW75C5Z]] and the [[linearity of differentiation|0M0TKFRX2A]].\nSo the derivative of a polynomial of degree $n \\ge 1$ is a polynomial of degree $n - 1$.\nMathlib states it as `Polynomial.hasDerivAt`.\n\n## Explanations\n\n### L1 human\n\nWe differentiate a polynomial term by term with the power rule.\nFor example, the derivative of $3 x^2 + 5 x + 7$ is $6 x + 5$.\n",
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