- calculus - Finding $\int x^xdx$ - Mathematics Stack Exchange
These identities for dx d x and dx d x are sometimes called the "sophomore's dream" Look that up on Wikipedia
- What does the dx mean in an integral? [duplicate]
The " dx d x " lets people think informally that you're multiplying a height, f(x) f (x), by an "infinitesimal width", dx d x, and then taking an infinite sum
- Is There a Difference Between $d^2x$ and $(dx)^2$?
Here, (dx)2 (d x) 2 means dx ∧ dx d x ∧ d x, and the fact that it vanishes comes from the fact that the exterior algebra is anti-commutative In other words, formally we have d2x = 0 d 2 x = 0 and (dx)2 = 0 (d x) 2 = 0 but for two different reasons
- 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
- 微分符号，dx，dy到底是什么含义？ - 知乎
其中一派被称之为 实无穷派，他们最大的特点认为无穷小量是一种实实在在的量，可以和其他实数一起参与代数运算，比如加减乘除，代入到基本函数里面。比如，实无穷派可以内心毫无波澜地写成下面的等式 dy=sin (x+dx)-sin (x)=2cos (x+\frac {dx} {2})sin (\frac {dx} {2})\approx cos (x)dx 另外，无穷小量和实数
- 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。如果微观的话，dy dx与f (x)在m点的切线T斜率（也就是导数值）f'并不相等。中间差
- 究竟如何理解 dx？ - 知乎
所以针对楼主问题的答案，什么是dx，dx就是自变量的微分，它等于一个无穷小量，既然是自变量的微分，就可以进行各种运算，比如3dx=d3x一样。 但是永远别忘了，有一个高阶无穷小的存在，很多定理的证明，都需要考虑这个无穷小量，就像链式法则的证明一样。
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