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  • derivatives - Proof of dy=f’(x)dx - Mathematics Stack Exchange
    Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
  • Integral of $dy dx$ confusion - Mathematics Stack Exchange
    $\begingroup$ Well, formally you may not be allowed to, yet practically you are The difference is that in basic mathematics the expression $\;\frac{dy}{dx}\;$ is one single thing, not a fraction, yet when we work with differentials we see we can actually take them, in cases like this one, as fractions and separate their numerator, denominator and etc
  • 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
  • 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
  • calculus - Rigorously, whats happening when I treat $\frac {dy} {dx . . .
    The reason why $~dy dx~$ behave "Fraction-like", is because they are limits of things that are fractions This does not imply that $~dy dx~$ is a fraction, but rather that sometimes the manipulations that we do to fractions survive through the limiting process, giving us one of these main theorems But each time, it is a nontrivial result and
  • Why should dy dx always be the tangent of the inclination?
    $\frac{dy}{dx}$ is, by definition, the limit of a secant line as the distance between two points approaches zero - it simply is the slope, nothing more to prove really (other than that the derivative actually exists, which is beyond the scope of this question)
  • 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?





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