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Proof that total derivative is the only function that can be added to Lagrangian without changing the EOM So I was reading this:  and while the answers for the first question are good, nobody gave much attention to the second one. In fact, people only said that it can be proved without giving any proof or any.  So, if I have a Lagrangian and ADD an arbitrary function of $\dot{q}$, $q$ and $t$ in such a way that the equations of motion are the same, does this extra function MUST be a total time derivative?   EDIT Ok, I changed my question a little bit:  Question: If I have a function that obeys the Euler-Lagrange equation off-shell, this implies that my function is a time derivative? (This was used in Qmechanic's answer of this other question: , equation 14.)  Also, why people only talk about things that change the Lagrangian only by a total derivative? If this is not always the case that keeps the equation of motion the same, so why is it so important? And why in the two questions I posted about the same statement on Landau&amp;Lifshitz's mechanics book only consider this kind of change in the Lagrangian? set 4-bit nibble in an int type Does a non-EU Spouse of a UK national need a visa to visit the Schengen area? I am a British national resident in the UK. My wife is Jordanian, resident in the UK with me. She has a UK biometric residency permit. We were married in the UK and the marriage is registered in the UK.   Does my wife need visas to travel with me on holiday in France and Spain? I understand from EU Directives that she does not. Would we be able to leave the UK by ferry to France if my wife does not have a French visa but can prove that she is married to me and resident in the UK? If visas are necessary but the French or Spanish consulates were NOT to grant the visas, would this be in contravention of EU Directives/Law? If the answer to question 3 is "Yes, it would be unlawful", what action can one take to get the visas? How do I grant sudo privileges to an existing user? I want to grant a newly created user sudo privileges in Ubuntu.  I tried  sudo adduser hduser admin   but it says no admin group exists. How can I do it? Leaving the States on Visa Waiver and coming back I'm travelling on the ESTA visa waiver, I'm now in the States but would like to go to Costa Rica for a bit (say three weeks) then come back to the States. All will be within my 90 day limit.  Is that allowed?  (I have my onward ticket home.) I have a Dell Inspiron 1525 laptop and I am planning on purchasing a mac mini, new version , I am tight on money for a while and want to use my current laptop screen as monitor for mac mini, I just want to know if it is at all possible to do, I have windows 7 and ubuntu 11.04 installed in my laptop, and I don't really care if need to wipe them out, or purchasing a monitos is the only option left, also I am planning to use it for coding and stuff, so VNC is probably not a good choice. Please help me to prove this trigonometric equation.  $\cos \left( 36^\circ \right)-\cos \left( 72^\circ \right) = \frac{1}{2}$  Thank you. Notation of the second derivative - Where does the d go? In school I was taught that we use $\frac{du}{dx}$ as a notation for the first derivative of a function $u(x)$. I was also told that we could use the $d$ just like any variable. After some time we were given the notation for the second derivative and it was explained as follows: $$ \frac{d(\frac{du}{dx})}{dx} = \frac{d^2 u}{dx^2} $$ What I do not get here is, if we can use the $d$ as any variable, I would get the following result: $$ \frac{d(\frac{du}{dx})}{dx} =\frac{ddu}{dx\,dx} = \frac{d^2 u}{d^2 x^2} $$ Apparently it is not the same as the notation we were given. A $d$ is missing. I have done some research on this and found some vague comments about &quot;There are reasons for that, but you do not need to know...&quot; or &quot;That is mainly a  notation issue, but you do not need to know further.&quot; So what I am asking for is: Is this really just a notation thing? If so, does this mean we can actually NOT use d like a variable? If not, where does the $d$ go? I found  related question, but it does not really answer my specific question. So I would not see it as a duplicate, but correct me if my search has not been sufficient and there indeed is a similar question out there already. Korea: Visa required to go to the city while in transit in Seoul for a Philippine citizen? Mail App keeps popping up in the background in Mac OS Mojave How many solutions has the equation $\sin x= \frac{x}{100}$ ? How many solutions has the equation $\sin x= \frac{x}{100}$ ?   Usually when I was asked to solve this type of problem, I would solve it graphically but this one seems to be trickier. It doesn't seem wise to put $f(x)=\sin x$ and $g(x)=\frac{x}{100}$ in the same graph and then counting all the intersection points.  What would be some algebraic methods to solve this? I found this confusing when I use the neural network toolbox in Matlab. It divided the raw data set into three parts:   training set validation set test set   I notice in many training or learning algorithm, the data is often divided into 2 parts, the training set and the test set.  My questions are:   what is the difference between validation set and test set?  Is the validation set really specific to neural network? Or it is optional. To go further, is there a difference between validation and testing in context of machine learning? Existence of elements of order $p^k$ in a finite group By Cauchy's theorem, if a prime number $p$ divides the order of a group $G$, then there is an element $g$ in $G$ whose order is $p$. In addition, if $|G|$ admits a prime decomposition with a factor $p^k$, then Sylow's theorem tells us that a subgroup of order $p^k$ must exist.   My question is the following. If $|G|$ admits a prime decomposition with a factor $p^k$, does this imply that an element of order $p^k$ must exist in $G$?   Update: As explained in Mindlack's answer (among others), the implication does not hold and simple counterexamples exist. In the comments, Mindlack discusses special cases where such an element exists. We have two iPads, and both of them have Minecraft PE. My son wants to connect the two and play with me. I have absolutely no idea what I am doing here, so I do not know how to do this.   One game says "Broadcast to LAN", and the other one says "Local Server Multiplayer". I have switched both to on.   What do I need to do to be able to play joined? We are both on the same WiFi. I just know that ls -t and ls -f give different sorting of files and subdirectories under a directory.   What are the differences between timestamp, modification time, and created time of a file? How to get and change these kinds of information by commands? In terms of what kind of information do people say a file is "newer" than the other? What kinds of information's change will not make the file different?   For example, I saw someone wrote:     By default, the rsync program only looks to see if the files are different in size and timestamp. It doesn't care which file is newer, if it is different, it gets overwritten. You can pass the '--update' flag to rsync which will cause it to skip files on the destination if they are newer than the file on the source, but only so long as they are the same type of file. What this means is that if, for example, the source file is a regular file and the destination is a symlink, the destination file will be overwritten, regardless of timestamp.   On a side note, does the file type here mean only regular file and simlink, not the type such as pdf, jpg, htm, txt etc? Polar Plot x and y ticks and units I've tried to setup an autologin, but that isn't possible, because my home is encrypted. What are the reasons for this?  PS. Here I have described my problem: . How many edges does an undirected tree with $n$ nodes have? More than 9 hundred as hundreds? In German, we often use "Elfhundert" (literally, "eleven hundred") for 1100 or "neunzehnhundert" ("nineteen hundred") for 1900; but is this correct in English? Putting a table next to a figure