derivative of inseparable equation Is there a way to find the derivative of an equation where I cannot separate the independent variable from the dependent variable. For example, what is $dy/dx$ given  \begin{equation*} \cos(y) = \dfrac{x}{x+y} \end{equation*}
Implicit Differentiation Help I have to use implicit differentiation to find $\frac{dy}{dx}$ given:  $$x^2 \cos(y) + \sin(2y) = xy$$  I don't even know where to begin, I missed the class where we went over implicit differentiation, and because of that, I am completely stuck.   Thank you everyone.  Edit: I don't know how to make the equation look all nice and whatnot, so sorry about that
How to setup OpenVPN Client For example,   If this van's a-rockin', don't come a-knockin'  (song title)   (song title)   I have a few related questions:   What is the "a-" or "-a" called? Is there a function beyond a rhythmic one? Why is "a-" attached to a word at all -- and why attach to a word at all? Grep: unexpected results when searching for words in heading from man page I'm running into weird behavior when trying to grep a man page on macOS. For example, the Bash man page clearly has an occurrence of the string NAME:  $ man bash | head -5 | tail -1 NAME   And if I grep for name I do get results, but if I grep for NAME I don't:  $ man bash | grep 'NAME' $ man bash | grep NAME   I've tried other uppercase words that I know are in there, and searching for SHELL yields nothing whereas searching for BASH yields results.  What's going on here?  Update: Thanks for all the answers! I thought it worth adding the context in which I ran into this. I wanted to write a bash function to wrap man and in cases where I've tried to look up the man page for a shell builtin, jump to the relevant section of the Bash man page. There might be a better way, but here's what I've got currently:  man () {   case "$(type -t "$1")" in     builtin)       local pattern="^ *$1"        if bashdoc_match "$pattern \+[-[]"; then         command man bash | less --pattern="$pattern +[-[]"       elif bashdoc_match "$pattern\b"; then         command man bash | less --pattern="$pattern[[:&gt;:]]"       else         command man bash       fi       ;;     keyword)       command man bash | less --hilite-search --pattern='^SHELL GRAMMAR$'       ;;     *)       command man "$@"       ;;   esac }  bashdoc_match() {   command man bash | col -b | grep -l "$1" &gt; /dev/null } I want to pose a question such as:  What is your name? Joe  How would I accomplish this using Console.WriteLine to also wait for the response on that same line instead of it being broken into:  What is your name? Joe Disable display of passwords on an iPhone? Once you have defined a passcode to unlock an iPhone, and for every application asking a password, when waiting for a password an iPhone makes a transient display of any character you type. It is clear that this transient display was purposefully set in place to help people who have problems with passwords or with the on screen keyboard. This transient display lasts 3 seconds to avoid too big a security problem. But this is still largely sufficient for anyone behind you to read it really easily. Moreover this transient display can be easily captured by any camera or by a software on the iPhone:    I evaluate this echo of any password as a serious risk. This echo partially exposes a secret.  Is there any simple configuration method to suppress everywhere this mechanism of transient display of any password?    For information, I reported this security problem at :     Once I have defined a passcode to protect my iPhone, and within every   application asking me a password, when entering my password iOS makes   a transient display of any character I type. I guess that this   transient display of passwords was purposefully set in place to help   people who have problems with passwords or with the on screen   keyboard. This transient display lasts 3 seconds to avoid to create   too serious a security problem. But this is still amply sufficient for   anyone behind you to read it really easily.      This transient display can be easily captured by a camera   surreptitiously activated by a malicious neighbour.      I didin't find any easy way to block this security weakness with iOS 7   up to iOS 9.      How to disable this transient display of any password on iOS? Non-uniform distribution of p-values when simulating binomial tests under the null hypothesis I heard that under the null hypothesis the p-value distribution should be uniform. However, simulations of binomial test in MATLAB return very different-from-uniform distributions with mean larger than 0.5 (0.518 in this case):   coin = [0 1]; success_vec = nan(20000,1);  for i = 1:20000     success = 0;     for j = 1:200         success = success + coin(randperm(2,1));     end     success_vec(i) = success; end      p_vec = binocdf(success_vec,200,0.5);     hist(p_vec);   Trying to change the way in which I generate random numbers didn't help.  I would really appreciate any explanation here. How to write (La)TeX (with parentheses) [or any other TeX-related logo] Prove that $\frac{a_1^2}{a_1+a_2}+\frac{a_2^2}{a_2+a_3}+ \cdots \frac{a_n^2}{a_n+a_1} \geq \frac12$ Let $a_1, a_2, a_3, \dots , a_n$ be positive real numbers whose sum is $1$. Prove that $$\frac{a_1^2}{a_1+a_2}+\frac{a_2^2}{a_2+a_3}+ \ldots +\frac{a_n^2}{a_n+a_1} \geq \frac12\,.$$  I thought maybe the Cauchy and QM inequalities would be helpful. But I can't see how to apply it. Another thought (might be unhelpful) is that the sum of the denominators on the left hand side is $2$ (the denominator on the right hand side). I would really appreciate any hints. From the movies we know that Obi-Wan Kenobi delivered Luke Skywalker to Owen and Beru Lars to raise on Tatooine shortly after Luke was born at the end of RotS (Episode 3).   The next think we know is Luke running into Ben Kenobi during A New Hope.   There seems to be a hint that there was at least SOME communication between Kenobi and Lars family based on him telling Luke:     Your father wanted you to have this when you were old enough, but your uncle wouldn't allow it.   (though it's possible that was referring to Kenobi offering to leave the lightsaber to Larses at the same time he dropped off Luke)  I was wondering if any details of what transpired between Kenobi and Larses in the years between RotS and ANH were noted in any canonical works (of any canon, including EU books/games/comics/etc...)? How do I Sort a Multidimensional Array in PHP Let $M,N$ be $n \times n$ square matrices over an algebraically closed field with the properties that the trace of both matrices coincides along with all powers of the matrix. More specifically, suppose that $\mathrm{Tr}(M^k) = \mathrm{Tr}(N^k)$ for all $1\leq k \leq n$. The following questions about eigenvalues is then natural and I was thinking it would be an application of Cayley-Hamilton but I am having trouble writing out a proof.  How do we show that $M$ and $N$ have the same eigenvalues?  Added (because this question is now target of many duplicates, it should state its hypotheses properly). Assume that all the mentioned values of $k$ are nonzero in the field considered; in other words either the field is of characteristic $0$, or else its prime characteristic $p$ satisfies $p&gt;n$. Disable UpdateOrchestrator Reboot task How do I add a border around windows but keep the current theme? I seem to live my life in the terminal - many terminals in-fact.  I also love the Ambiance theme - but the new borderless windows does not provide the visual differentiation I'm used to (the same black windows appear to blend into each other).    Thus to my question - how do I add back the single pixel border for windows that is found in earlier Ubuntu versions?  I want to keep the Ambiance overall theme since this looks good and I dont want to swap to another theme.      Now I know that I can modify the Ubuntu Ambiance theme as follows:  mkdir ~/.themes cp -r /usr/share/themes/Ambiance .themes   Then flipping between the theme options in the Settings - Appearance picks up changes in the theme in now in the .themes folder.  I presume I need to alter one of the .css files but I dont know which one.  I was also looking at  but the solutions there doesnt work for 14.04.  I also looked at the  but got rather lost trying to figure out which one applies to my situation. $1^n +2^n + \cdots +(p-1)^n \mod p =$? Calculate for every positive integer $n$ and for every prime $p$ the expression  $$1^n +2^n + \cdots +(p-1)^n \mod p$$    I need your help for this. I don't know what to do, but I'll show you what I know.   Wilson's theorem The identity $X^p-X = \prod_{a \in \mathbb{F}_p-1}(X-a)$ $\exists a \in \mathbb{Z}, \ a^2 \equiv -1 \mod p \qquad \iff \qquad p \equiv 1 \mod 4$   Now can you please provide me a hint? Code coverage for wrapper class is 0% I have written below Wrapper class.  global class BI_VA_AutomationWrapper {      global class BI_VA_AutomationRequest {      webservice String userName;     webservice String emailId;     webservice String buinessUnit;     webservice String orgName;     webservice String country;     webservice String environment;     webservice String myShopNumber;     webservice String BidsId;//for testing     webservice String Type; //for testing  }  global class BI_VA_AutomationResponse {      webservice String responseStatus;     webservice String myShopNumber;     //webservice list&lt;Error&gt; errorMessages;     webservice String  errorMessages;//for testing   } global class BI_VA_Error {      webservice String type;     webservice String message;    }}   And test class is,  @isTest public class BI_VA_AutomationWrapperTestClass  { public static testMethod void unitTest(){      BI_VA_AutomationWrapper.BI_VA_AutomationRequest wrap= new BI_VA_AutomationWrapper.BI_VA_AutomationRequest();        wrap.userName='Test@test.com';     wrap.emailId='Test@test11.com';     wrap.buinessUnit='AH';     wrap.orgName='ORD';     wrap.country='US';     wrap.environment='QA';     wrap.myShopNumber='123456789';     wrap.BidsId='123';     wrap.Type='ResetPassword';              BI_VA_AutomationWrapper.BI_VA_AutomationResponse res= new BI_VA_AutomationWrapper.BI_VA_AutomationResponse();     res.responseStatus = 'Success';     res.myShopNumber = '987654321';     res.errorMessages = 'Test error';      BI_VA_AutomationWrapper.BI_VA_Error error = new BI_VA_AutomationWrapper.BI_VA_Error();     error.type = 'Test';     error.message = 'Test';  }}   Code coverage is 0% only. What is Snell's law's main formula? My book states it as $(\sin i)/(\sin r)=n$. However, University Physics has a different say.  It says, $n_{a} \sin a =n_{b} \sin b$. Which of the following is correct? Using conditional statements in ArcGIS Field Calculator? I have two fields, "P_Area" and "PC_Area", whose sizes I'd like to compare in a third field, "Areas_Equal". The "Areas_Equal" field should contain a "Yes" if the other two are equal and a "No" if they aren't.  How can I do this with Field Calculator and its Python Parser? How do I handle elastic contacts in a simulation with friction I'm trying to simulate a wheel as it hits the ground.  Problem 1  Suppose a disc is dropped from a height. It has initial velocity of $-x,-y$ caused by throwing and gravity. It has no initial angular velocity. When it hits the ground it should have some rotation resulting from the collision.   How to calculate force that caused torque for that rotation?   Problem 2  The same disc is dropped from height. It doesn't have velocity on the side direction. It already spinning fast. When it hits the ground the spinning should cause some translation.   How to calculate force that caused this linear acceleration? Some rotation must be lost in the collision, how to calculate that?   To simplify assume static $friction = 1$ and $g = -10$. How far can one get in analysis without leaving $\mathbb{Q}$? Suppose you're trying to teach analysis to a stubborn algebraist who refuses to acknowledge the existence of any characteristic $0$ field other than $\mathbb{Q}$.  How ugly are things going to get for him?  The algebraist argues that the real numbers are a silly construction because any real number can be approximated to arbitrarily high precision by the rational numbers - i.e., given any real number $r$ and any $\epsilon&gt;0$, the set $\left\{x\in\mathbb{Q}:\left|x-r\right|&lt;\epsilon\right\}$ is nonempty, thus sating the mad gods of algebra.  As @J.M. and @75064 pointed out to me in chat, we do start having some topology problems, for example that $f(x)=x^2$ and $g(x)=2$ are nonintersecting functions in $\mathbb{Q}$.  They do, however, come arbitrarily close to intersecting, i.e. given any $\epsilon&gt;0$ there exist rational solutions to $\left|2-x^2\right|&lt;\epsilon$.  The algebraist doesn't find this totally unsatisfying.     Where is this guy really going to start running into trouble?  Are there definitions in analysis which simply can't be reasonably formulated without leaving the rational numbers?  Which concepts would be particularly difficult to understand without the rest of the reals? Farkas/guards pursuing me glitch I was doing a quest for the companions. When I entered Jorrvaskr, Farkas pulled out his sword and began to talk to me. Every time I would try to leave the conversation he would just follow me and try to talk to me again. This lead to me paralyzing Farkas and running away.   By the time I got to the gates of Whiterun he had already gotten up, ran to me and started another conversation. I quickly made it to the gates and exited, he followed me through the gates but I whirlwind sprinted to Shadowmere then attempted to fast travel - which game me the "Can not fast travel when guards are pursuing you" message even though no guards were following me.   I knew Farkas wasn't far behind so I quickly jumped on a carriage and I traveled to the nearest hold which was Dawnstar. Now I can't leave Dawnstar because the same message appears. I have tried to pay off my debt to the Dawnstar guards but it didn't fix the problem. How can I resolve this issue?