Welcome to 9math!

Posted September 18th, 2007 by Isoscel

This site is for those who are interested in mathematics, whether they want to study it for school or as a hobby.

If you have math questions you can ask them on the forum.

On this site you can write nice mathematical expressions and equations by using Latex and the visual Equation Editor:

$$\sum_{k=1}^{n}k^2=\frac{n(n+1)(2n+1)}{6}$$

You can use the mouse to play with the interactive geometry figures.

You can also draw functions' graphs fast:

If you wish to learn new notions and tricks you can read the documentation (Algebra, Analysis, Arithmetic, Geometry) that we are developing.

Look at the recent posts to keep up with the latest activity.

Also read the FAQ and Help for more information.

List of derivatives

Posted February 9th, 2009 by Structure
$$(x^n)'=nx^{n-1}$$
$$(lnx)'=\frac{1}{x}$$
$$(\sqrt x)'=\frac{1}{2\sqrt x}$$
$$(\sqrt[3] x)'=\frac{1}{3\sqrt[3] {x^2}}$$
$$(\sqrt[n] x)'=\frac{1}{n\sqrt[n] {x^{n-1}}}$$
$$(e^x)'=e^x$$
$$(a^x)'=a^x ln a$$
$$(e^{f(x)})'=e^{f(x)}f'(x)$$
$$ (\sin x)'=\cos x$$
$$ (\cos x)'=-\sin x$$
$$(\tan x)'=1+\tan^2x=\frac{1}{\cos^2x}$$
$$ (\cot x)'=-1-\cot^2x=-\frac{1}{\sin^2x}$$
$$(f(x)g(x))'=f'(x)g(x)+f(x)g'(x)$$
$$(\frac{f(x)}{g(x)})'=\frac{f'(x)g(x)-f(x)g'(x)}{g^2(x)}$$
$$(g(f(x)))'=g'(f(x)f'(x)$$

Surface integral in spherical coordinates

Posted January 29th, 2009 by Structure

Let us consider a surface integral

$$\int_{\Sigma}F(x,y,z)d\sigma$$

where $ \Sigma $ is a surface which have a parameterization described in terms of angles $ \theta $ and $ \phi $ in spherical coordinates.
Let
$ x=r \cos \theta sin \phi $
$ y=r \sin \theta \sin \phi $
$ z = r \cos \phi $
and let
$ \chi(r,\phi,\theta)=(r \cos \theta sin \phi, r \sin \theta \sin \phi,r \cos \phi) $
We are interested in a formula for evaluating a surface integral where r is a function of angular variables
$ r=\rho(\theta,\phi) $

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