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The right question is not what is a differential? but how do differentials behave? If i start with an ordinary ellipse equation \\begin{equation} \\frac{x^2}. Let me explain this by way of an analogy

Suppose i teach you all the rules for adding and multiplying rational numbers I want to derive an differential form for equation of an ellipse Then you ask me but what are the rational numbers? the answer is

They are anything that obeys those rules

Now in order for that to make sense, we have to know that there's at least. See this answer in quora What is the difference between derivative and differential? In simple words, the rate of change of function is called as a derivative and differential is the actual change of function

We can also define a derivative in terms of differentials as the ratio of differentials of function by the differential of a variable. I am a bit confused about differentials, and this is probably partly due to what i find to be a rather confusing teaching approach (i know there are a bunch of similar questions around, but none o. 69 can someone please informally (but intuitively) explain what differential form mean

What is difference between implicit and explicit solution of an initial value problem

Please explain with example both solutions (implicit and explicit)of same initial value problem What bothers me is this definition is completely circular I mean we are defining differential by differential itself Can we define differential more precisely and rigorously

Is it possible to define differential simply as the limit of a difference as the difference approaches zero? $$\mathrm {d}x= \lim_ {\delta x \to 0}\delta x$$ thank you in advance. The differential equations class i took as a youth was disappointing, because it seemed like little more than a bag of tricks that would work for a few equations, leaving the vast majority of interesting problems insoluble I am quite new to differential equations and derivatives

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