Oct 7, 2015 · $\begingroup$ @KristofferCatabui, I had sort of assumed that you had mis-used the notation for partial derivatives (the question was un-clear, and people frequently mis-use that).

Dec 17, 2019 · 再引入函数的外积，能够证明dx_i之间的外积，其中i的按照严格升序构成交错张量空间这个线性空间的基，这样就给出交错张量空间的元素用dx_i的外积表达，从而引入微分形 …

May 2, 2015 · We take $\frac{dy}{dx}$ as a symbol on its own that can't be slit up into parts. The symbol $$ \frac{d}{dx} $$ you can consider as an operator. You can apply this operator to a …

Historically, calculus was framed in terms of infinitesimally small numbers. The Leibniz notation dy/dx was originally intended to mean, literally, the division of two infinitesimals. The Leibniz …

In the setting of measure theory, "dx" is interpreted as a measure; in the context of differential geometry, it is interpreted as a 1-form. But, for the purposes of elementary calculus, the only …

Many people have pointed out that the integral you are looking for is equivalent to, $$\sum_{n}^{\infty} \frac{1}{n!} \int_{0}^{x}x^{n}\ln(x)^ndx$$

Jun 21, 2014 · 概念的话dx就是把定义域的x范围无限分（微分）其中的一份如x1 到x2 这一小段就是dx。 同理，dy就是值域的无限分为f(x2)-f(x1)。 dy/dx 是f(x)一个微分成dx dy围成的小三角 …

Aug 21, 2023 · 于是牛顿（和莱布尼兹）老爷子发现，在某一点，自变量增量 \mathrm dx 非常小的时候，这一点切线的增量 \mathrm dy 和 \mathrm dx 是呈线性关系的，也就是说 \mathrm dy …

Dec 27, 2013 · $\begingroup$ $∆x~$ is small change in $~x~$. $~dx~$ is small part of $~x~$ but represents independent change. & $~\frac{dy}{dx}~$ means slope of tangent at a point where …

Oct 1, 2021 · A new number system called hyperreal number system was introduced by him, which contains infinitesimals and infinities. According to that, An infinitesimal 'dx' is a number …