- calculus - dx(t) dx vs. dx dx - Mathematics Stack Exchange
$\begingroup$ @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)
- What does $dx$ mean? - Mathematics Stack Exchange
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 role of the "dx" is to tell which variable is the variable of integration
- What does the dx mean in an integral? [duplicate]
I know dy dx for example means "derivative of y with respect to x," but there's another context that confuses me You will generally just see a dx term sitting at the end of an integral equation and I just don't know exactly what it means or why it's there For instance, if I put into Wolfram Alpha "integral of 2x", it writes out: That dx in
- 导数符号中，dx 的含义是什么？ - 知乎
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围成的小三角形的tan值。等同于导数值。但这只是宏观上的。
- calculus - Finding $\int x^xdx$ - Mathematics Stack Exchange
Many people have pointed out that the integral you are looking for is equivalent to, $$\sum_{n}^{\infty} \frac{1}{n!} \int_{0}^{x}x^{n}\ln(x)^ndx$$
- What is $dx$ in integration? - Mathematics Stack Exchange
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 notation $\int f dx$ was meant to indicate a sum of infinitely many rectangles, each with infinitesimal width dx
- calculus - What is the true, formal meaning and reason for the dx . . .
Prior to the 1800s, "dx" was considered an "infinitesimal" - a number so close to zero that, for some things, it can be considered actually zero, but wasn't exactly zero In the 1800s, the failure to formalize infinitesimals (and, in my opinion, the growing rise of materialism) led to the belief that infinitesimals were invalid mathematical
- Is There a Difference Between $d^2x$ and $(dx)^2$?
However, what Thompson is trying to explain, might be more easily understood using finite differences After all, derivatives are limits of finite differences
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