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- calculus - What is the difference between $dy$ and $Δy$ and why is $dx . . .
For examples, this $\mathrm{d}y$ as $\delta y$ and $\mathrm{d}x$ as $\delta x$ notation is used in videos like the ones mentioned in a comment by the OP Yashasv Prajapati: blackpenredpen's “delta y vs dy (differential)” and The Math Sorcerer's “How to Compute Delta y and the Differential dy”
- In differential calculus, why is dy dx written as d dx ( y)?
In differential calculus, We know that dy dx is the ratio between the change in y and the change in x In other words, the rate of change in y with respect to x
- derivatives - Proof of dy=f’(x)dx - Mathematics Stack Exchange
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- What exactly are dx and dy in differential equations?
If I understand correctly, you mean if we have something like: $$\frac{dy}{dx}=f(y)g(x)$$ then we get: $$\int\frac{1}{f(y)}\frac{dy}{dx}dx=\int g(x)dx$$ writing it like this shows that we integrate wrt the same variable on both sides but it can be simplified to: $$\int\frac{dy}{f(y)}=\int g(x)dx$$ similarly if we have an expression of the form
- 老师说链式法则里某个 dy dx 不能理解为 dy 除以 . . . - 知乎
\frac{dx}{dy}={\left ( \frac{dx}{\color{Red}{ dt} } \right ) \Big \left ( \frac{dy}{\color{Red}{ dt}} \right ) } 这里与复合函数链式法则完全相同，由于 dx,dy 都是由 t 的变化而产生的无穷小量，因此仍然可以同时“乘”、“除” dt 。 鸣谢： 莱布尼茨发明的部分叙述参考了：Is dy dx not a
- 微分符号 dx、dy 表示什么含义？ - 知乎
dy = f'(x_0) \Delta x = f'(x_0)dx, 这里的含义是比较含混不清的 从数学的角度, 我们还是希望能够明确地从已知的概念定义微分到底是什么, 或者说, 包含于怎样的集合, 是怎么（构造）出来的, 而不是随手写一串字母给它取个名字, 连它包含在什么样的集合里, 这个集合
- Why is the 2nd derivative written as - Mathematics Stack Exchange
In Leibniz notation, the 2nd derivative is written as $$\dfrac{\mathrm d^2y}{\mathrm dx^2}\ ?$$ Why is the location of the $2$ in different places in the $\mathrm dy \mathrm dx$ terms?
- 高等数学中，dy 的「d」是什么意思？ - 知乎
dy中的d全称differential，代表y这个变量的很小的变化。 同理，dx中的d是指x这个变量的很小的变化。 最先发明这种符号的是德国数学家戈特弗里德·莱布尼茨。
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