论文标题
正式的差异变量和抽象链规则
Formal differential variables and an abstract chain rule
论文作者
论文摘要
链条规则的一个缺点是它不迭代：它给出了f（g（x））的导数，而不是（直接）第二或高级导数。我们介绍了迭代的差异和多变量链规则的版本，该规则将其迭代到任何所需的衍生物级别。我们首先是非正式地介绍此材料的，然后讨论如何使其严格（讨论，涉及微积分的正式基础）。我们还建议一个有限的演算链规则（与格雷厄姆，诺斯和帕塔什尼克的说法相反，他说“没有有限的微积分的链条规则”）。
One shortcoming of the chain rule is that it does not iterate: it gives the derivative of f(g(x)), but not (directly) the second or higher-order derivatives. We present iterated differentials and a version of the multivariable chain rule which iterates to any desired level of derivative. We first present this material informally, and later discuss how to make it rigorous (a discussion which touches on formal foundations of calculus). We also suggest a finite calculus chain rule (contrary to Graham, Knuth and Patashnik's claim that "there's no corresponding chain rule of finite calculus").
