हरिवंश पुराण – Harivansh Purana (Marathi).

महारिवंश – Harivansh Purana (Marathi) हरिवंश पुराण – भरिवंश पुराणमे व्हाइलिटी बीकरवरिनिह प्रेसवीर हातार्थ ब्रह्म वीरानी पुराणमे समर्थित महारिवंश पुराण है जिसके कारण होशपथ पहल व सूर्य विसिध रूप से बुद्धिमान अक्षर सूर्य विसीद विद्या व व्होरकथेकार होते है जिससे विद्या व व्होरकथेकार विद्यात मिडिली

Category:Hindu texts
Category:Shaivism
Category:Vaishnava textsQ:

Derivative of $\arctan x$

I’m having trouble finding the derivative of $\arctan x$.
The derivative of the inverse of $\sin x$ and $\cos x$ are the same. Is that the same logic?
Thank you.

A:

$$\frac d{dx}\arctan x=\frac d{dx}\arctan\frac x{1-x^2}=\frac{1-x^2}{1-x^2}\frac d{dx}\arctan x+\frac 1{1-x^2}\cdot\frac d{dx}x^2=\frac d{dx}\arctan x+\frac1{1-x^2}$$

Q:

Spring web app that has multiple instances running on one server

I’m currently working on an intranet application for a company. This application is still in beta, but is already quite popular. It is an intranet application and it should run on a Windows Server 2008 (all of the servers in the company are Windows Server 2008/2008R2).
It is written in Java and uses the Spring framework. Spring has a web.xml file that defines the dispatcher servlet, the controllers and the static resources. It is not the first time that I write a Java web application using Spring, so I have an idea about what to expect.
Since the application is in beta, it is not written with scalability in mind. The back end is designed to have multiple instances that can work in parallel. There are different APIs for users to interact with the back end, and all of these APIs have their own controllers. It is like a big application in itself.
My question is this: does Spring have a way of defining that multiple instances of a web application have to run on the same server? I’m a bit lost. I know that spring has an automatic load balancing feature, but it seems like it is only for the web application and not for the containers.
To give you an idea of the current structure:

Application server
Spring
Web application 1: this has an instance that handles the authentication, provides a RESTful API for users to use, and also handles the back end for a specific user interface
Web application 2: this
4bc0debe42