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- 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 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
- 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
- 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
- calculus - Finding $\int x^xdx$ - Mathematics Stack Exchange
Many people have pointed out that the integral you are looking for is equivalent to, $$\sum_{n}^{\infty} \frac{1}{n!} \int_{0}^{x}x^{n}\ln(x)^ndx$$
- calculus - 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
- 不定积分符号为什么是∫dx？为什么要加一个dx？是不是多此一举了？ - 知乎
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 是 \mathrm dx 的线性函数。也就是我们知道的 \mathrm dy=f'(x_0)\mathrm dx 这是一个线性函数。
- calculus - Why are derivatives specified as $\frac{d}{dx . . .
Is the purpose of the derivative notation $\frac{d}{dx}$? strictly for symbolic manipulation purposes? I remember being confused when I first saw the notation for derivatives - it looks vaguely like there's some division going on and there are some fancy 'd' characters that are added in
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