Integral of $ (d^2y dx^2) dy$ - Mathematics Stack Exchange I saw this as a step in a calculation and it was confusing The left cancels down to: $$\int \frac {d^2y} {dx^2}dy$$ But surely the answer is $\frac {d^2y} {dx^2}y$; instead, $\frac {d^2} {dx^2}$ is being
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 ”
Separable differential equations: detaching dy dx [duplicate] I'm just learning about differential equation separability I understand what a derivative is One notation for derivative is $\\frac{dy}{dx}$, which - misleadingly - is not a fraction Since it's n
高数刚学到微分，不明白为什么课本直接就让Δx=dx，Δy和dy都不一样，为什么它俩就可以相等？ - 知乎 我们再次梳理 d x, Δ x, d y, Δ y dx,\Delta x,dy,\Delta y 的关系 其中增量 Δ x, Δ y \Delta x,\Delta y 分别称作自变量和因变量的差分， d x, d y dx,dy 分别是自变量和因变量的微分 对于 Δ x \Delta x ，作为自变量的增量，我们不需要过多描述。 对于 d x dx ,，我们令 f (x) = x f (x)=x 时， d x = f ′ (x) Δ x → d x = Δ x dx=f' (x
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
d^2y dy ^2有什么区别？ - 知乎 而d (dy)，先看括号内的，指对y的微分，令dy=u，则d (dy)变为du，即对u求微分，所以我们可以推导出来，ddy就是对y求微分再求微分，即把一段y分成无数小块，取其中一块dy再把这个dy分成无数小块，取其中一块就是ddy或者写成d^2y，d^2可以理解为求两次微分，后面接