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  "body": "\n## Summary\n\nThe delta derivative is the derivative of [[time-scale calculus|30G1M35TK1]], defined for functions on a time scale, that is, on a nonempty closed subset of $\\R$.\nAt a point that is a limit from the right it is the usual derivative.\nAt a point isolated on the right it is a difference quotient across the gap.\nOn $\\R$ it is the ordinary [[derivative|0V1EJCT8G6]], and on $\\Z$ it is the forward difference, so it unifies differential and difference equations.\n\n## Explanations\n\n### L1 human\n\nPicture a time line in which some stretches are continuous and some moments are separated by gaps.\nAt a moment followed by a gap, the delta derivative compares the value now with the value at the next moment, and divides by the length of the gap.\nAt a moment with no gap to its right, it is the usual slope.\nFor example, on the time scale $2\\Z = \\set{\\dots, -2, 0, 2, 4, \\dots}$, the delta derivative of $f(t) = t^2$ is $\\frac{(t+2)^2 - t^2}{2} = 2t + 2$.\n",
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