# Tagged Questions

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### What's the difference between $\frac{\partial f}{\partial x}(x,y)$ and $\frac{\partial f (x,y)}{\partial x}$?

Is there a difference in the meaning of $\frac{\partial f}{\partial x}(x,y)$ and$\frac{\partial f (x,y)}{\partial x}$ or is it just a different notation for exactly the same thing?
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### How to determine the differentiability of a piece-wise defined function?

How should one test for differentiability of a function that is piecewise defined? How is the differentiability related to one sided derivative in this case? Also, in the limits $\lim_{h\to 0^+}$ ...
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### Why does $d$ mean?

What do the $d$'s mean? I've seen them in other formulas as well.
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### Chain Rule: Is the notation $\frac{dy}{du} \cdot \frac{du}{dx} = \frac{dy}{dx}$ accurate?

My question is if it is okay / mathematically rigorous to write the Chain Rule like that (the Leibniz way). I thought that $dx$, etc. do not follow the rules of algebra and cannot be treated as such. ...
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### Why are there so many notations for differentiation?

There are so many notations for differentiation. Some of them are: $$f^\prime(x) \qquad \frac{d}{dx}(f(x))\qquad \frac{dy}{dx}\qquad \frac{df}{dx}\qquad D f(x)\qquad y^\prime\qquad D_x f(x)$$ Why ...
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### Notation for function compositions/derivatives

When given $(f \circ g)'(0)$, does it mean to compose the 2 functions first, then take the derivative of the composed functions and evaluate it at $0$, or take the derivative of $g$ first and evaluate ...
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### What does the notation $Dx(a-bi-x)$ mean?

Sorry for completely newbie question, but could not the answer anywhere else. On the Wikipedia page about "Steiner inellipse" there is the following notation equating roots of cubic polynomial and ...
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### Using both Leibniz' notation and prime-notation for a derivative

I am presented with the following task: "Assume that the function $f(x)$ has the derivative $f'(x) = \frac{1}{x}$ and that $f$ is one-to-one. If $y = f^{-1}(x)$, show that $\frac{dy}{dx} = 1$. The ...
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### Abbreviation for $n$ times differentiable, with $n$th derivative bounded?

Are there convenient abbreviations in use for the following sets? The set of functions which are $n$ times differentiable, with first $n-1$ derivatives continuous (obviously the last part is ...
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### Does differentiation symbol need parentheses or?

Suppose I have this expression: $$\frac{d}{dx}(e^{x})^2 + 6$$ Does it mean to differentiate $6$ too or just the first term? This is an exercise on a calculus course that I'm doing on Coursera. ...
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### What exactly does the $d$ represent in $\frac{d}{dx}$?

When taking the derivative, such as $\frac{d}{dx}$, what exactly does the $d$ represent? The best answer so far is in for example $\frac{dy}{dx}$, the $d$ stands for change in and what follows the ...
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### Notation of derivative

When I studied derivative, I sometimes saw notation $\frac{d}{dx}2x=2$ and sometimes $\frac{\partial}{\partial x}2x=2$. What is the definition and difference between those notations?
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### Help with odd partial derivatives in velocity $\bar v^2 = \dot x ^2+\dot y^2$

I am doing a physics -course Tfy-0.2061. My teacher claims that this is velocity squared, $\bar v^2 = \dot x ^2+\dot y^2$. I cannot understand why it is not $\bar v^2 = (\dot x +\dot y)^2$. If ...
### What is the difference between $d$ and $\partial$?
After seeing the following equation in a lecture about tensor analysis, I became confused. $$\frac{d\phi}{ds}=\frac{\partial \phi}{\partial x^m}\frac{dx^m}{ds}$$ What exactly is the difference ...