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- 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
- What is $dx$ in integration? - Mathematics Stack Exchange
If f(x) f (x) is in meters per second and dx d x is in seconds, then f(x)dx f (x) d x is in meters, and so is the integral These things should be dimensionally correct, and are not so without the " dx d x " Sometimes one has a dot-product or a cross-product or a matrix product or some other sort of product between f(x) f (x) and dx d x
- 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
- 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。
- Limit of $\\frac{x^c-c^x}{x^x-c^c}$ as $x \\rightarrow c$
Here we have used that d(xx) dx = x ⋅xx−1 +xx ln(x) d (x x) d x = x x x 1 + x x ln (x), which can be directly evaluated (i dont remember the name of the theorem) and also by taking logarithms
- 高数中d dx和dy dx有什么区别？ - 知乎
d dx后面肯定跟这个括号 例如d dx (x²+1) 其实也就是让你求fx式子中对x的导。也就是 dx dy=d dx (f (x))=f' (x),表达方式不同而已。
- integration - How does one integrate $\int \cos (x^2) dx$ - Mathematics . . .
How does one integrate ∫ cos(x2)dx ∫ cos (x 2) d x? I have thought about using standard techniques of 'integration by parts' and 'partial fractions' but neither of them work I tried plugging it into Wolfram Alpha and I got π2−−√ C 2 π−−√ + π 2 C 2 π + a constant I am confused as to what the C C is supposed to mean and how to evaluate this intergral Thank you in advance
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