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- What do the symbols d dx and dy dx mean? - Mathematics Stack Exchange
Okay this may sound stupid but I need a little help What do d dx d d x and dy dx d y d x mean? I need a thorough explanation Thanks
- What is the difference between $dy$ and $Δy$ and why is $dx$ is same as . . .
For examples, this dy d y as δy δ y and dx d x as δx δ 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 Then, why is dy dx written as d dx
- dy dx . . . what are we really saying? What is dx? [duplicate]
Additional Note: When given an equation like: dy dx = 2x d y d x = 2 x You could re-write it as: dy = 2xdx d y = 2 x d x If you integrate the left hand side with respect to y y and the right hand side with respect to x x, you get y =x2 + c y = x 2 + c In this process one may be lead to think that dx d x is a variable
- What exactly are dx and dy in differential equations?
In undergraduate differential equations courses, calculations that involve manipulating dx d x and dy d y as independent quantities can always be rephrased easily to avoid doing so (That said, "infinitesimal intuition" should not be thrown out the window For intuition, we can think of dx d x and dy d y as tiny but finite quantities and do calculations with them, obtaining approximate
- Why is the 2nd derivative written as - Mathematics Stack Exchange
Here, the numerator represents d(dy) d (d y), or just the "operation" d() d () being performed on y twice, thus we can write it as d2y d 2 y In constrast, the denominator represents squaring dx d x Since dx d x is one "variable", we can remove the parentheses, resulting in the term dx2 d x 2
- 老师说链式法则里某个 dy dx 不能理解为 dy 除以 . . . - 知乎
帮忙找出链式法则里一处笔误。 关于莱布尼茨记号的历史实在是太长了，有很多数学家的工作在里面，包括Bernoulli兄弟在内的大数学家在后来都对此进行了完善。有兴趣的同学可以去看《古今数学思想》第二册82-92页。
- derivatives - Proof of dy=f’ (x)dx - Mathematics Stack Exchange
It's merely a symbolic notation, used to simplify some expressions If you will, just take dy = f′(x)dx d y = f ′ (x) d x as the definition of the symbols dy, dx d y, d x Note that these (at least for now) are no real mathematical objects (in the sense that they are rigorously defined), and just serve to make some stuff a bit tidier
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