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### Definition of e [duplicate]

Possible Duplicate: Why is $1^{\infty}$ considered to be an indeterminate form Is $dy/dx$ not a ratio? I'm very eager to know and understand the definition of $e$. Textbooks define $e$ as ...
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### What is wrong with treating $\dfrac {dy}{dx}$ as a fraction? [duplicate]

If you think about the limit definition of the derivative, $dy$ represents $$\lim_{h\rightarrow 0}\dfrac {f(x+h)-f(x)}{h}$$, and $dx$ represents $$\lim_{h\rightarrow 0}$$ . So you have a ...
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### $dy\over dx$ is one things but why in integration we can treat it as 2 different terms [duplicate]

when i am learning differentiation, my lectuer tell us that the deriative $dy\over dx$ is one things, it is not the ration between dy and dx. However when i learn about integrating, sometime we need ...
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### How do we go from $f'(x) = \frac{dy}{dx}$ to $dy = f'(x)dx$? [duplicate]

As far as I know, the derivative of $y$ is defined as: $$f'(x) = \lim_{h \rightarrow 0} \frac{f(x + h) - f(x)}h = \frac{dy}{dx}$$ So $\frac{dy}{dx}$ is a limit, not a fraction of real numbers. I ...
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### Why is $\frac {dy}{dx}$ treated as a fraction? Plus an implicit differentiation question. [duplicate]

Why is $\frac {dy}{dx}$ treated as a fraction? I always thought that it is just notation for the derivative of $y$ with respect to $x$, but when it comes to implicit differentiation and integration ...
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### What are some conceptualizations that work in mathematics but are not strictly true?

I am having an argument with someone who thinks that it's never justified to teach something that is not strictly correct. I disagree: often, the pedagogically most efficient way to make progress is ...
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### What is $dx$ in integration?

When I was at school and learning integration in maths class at A Level my teacher wrote things like this on the board. $$\int f(x)\, dx$$ When he came to explain the meaning of the $dx$, he told us ...
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### What is the practical difference between a differential and a derivative?

I ask because, as a first-year calculus student, I am running into the fact that I didn't quite get this down when understanding the derivative: So, a derivative is the rate of change of a function ...
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### Is $dx\,dy$ really a multiplication of $dx$ and $dy$?

On the answers of the question Is $\frac{dy}{dx}$ not a ratio? it was told that $\frac{dy}{dx}$ cannot be seen as a quotient, even though it looks like a fraction. My question is: does $dxdy$ in the ...
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### What does $dx$ mean?

$dx$ appears in differential equations, such us derivatives and integrals. For example, a function $f(x)$ its first derivative is $\dfrac{d}{dx}f(x)$ and its integral $\displaystyle\int f(x)dx$. But ...
We know that the chain rule is used to differentiate a composite function ,say $$f(x) = h(g(x))$$ It's defined as the derivative of the outside function times the derivative of the inner function or ...