May 2, 2015 · The symbols d/dx and dy/dx represent derivatives in calculus, indicating rates of change with respect to a variable.

Jul 31, 2022 · I was working with something and have the term ${dy\over dx}\times {dx\over dy}$. In my equality, it must to be $1$, so I try to prove it using the chain rule as follow: $${dx\over dx} = 1$$ $${dx\over dx} = {d\over dx}(f^{-1}(\ f(x)\ )\ ) = {df^{-1}(f(x))\over df(x)}\times {df(x)\over dx}$$

Apr 8, 2018 · Derivatives: First off, let's start with the derivative. This is commonly referred to as an "instantaneous rate of change", which is a complete oxymoron.

That is, dy is equal to the difference in the y value (f(x+h) - f(x)) and dx is equal to the difference in the x value (h) and dy/dx is equal to the rate of change of the y function as the x function increases. As well as this, in the chain rule you multiply dy/du * du/dx in order to cancel out the du's like you would with normal fractions.

May 10, 2020 · $${dy \over (dx)^2}={2x \over dx}+1$$ Now in this example the ${2x \over dx}$ term becomes infinity and therefore the expression makes no sense, but I am wondering is there any case that doing a similar thing would make sense and there is a …

Sep 16, 2024 · So we have (dy/dx)(x^2)=(2xi+i^2)/i. The denominator "i" comes as an infinitesimal by definition. The square of an infinitesimal, and the product of a real (or finite number) and an infinitesimal comes as an infinitesimal (see Keisler's book in anon's statement).

Jul 31, 2020 · 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, 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.

Mar 10, 2019 · The first question in your title is. What are differential equations? The informal answer is that often what we know about a quantity we are interested in is its rate of change.

Dec 15, 2013 · Ask questions and share your thoughts on the future of Stack Overflow. Join our first live community AMA this Wednesday, February 26th, at 3 PM ET.