Derivative of arcsin In my assignment I need to analyze the function 
$f(x)=\arcsin \frac{1-x^2}{1+x^2}$
And so I need to do the first derivative and my result is: 
$-\dfrac{4x}{\left(x^2+1\right)^2\sqrt{1-\frac{\left(1-x^2\right)^2}{\left(x^2+1\right)^2}}}$
But in the solution of this assignment it says 
$f'(x)=-\frac{2x}{|x|(1+x^2)}$
I don't understand how they get this. I checked my answer on online calculator and it is the same.

You should have developed your result a bit more to obtain the assignment solution.
\begin{align}
-\frac{4x}{(x^2+1)^2\sqrt{1-\frac{(1-x^2)^2}{(x^2+1)^2}}}&=-\frac{4x}{(x^2+1)^2\sqrt{\frac{x^4+1+2x^2-1-x^4+2x^2}{(x^2+1)^2}}} \\
&=-\frac{4x}{(x^2+1)^2\sqrt{\frac{4x^2}{(x^2+1)^2}}}\\
&=-\frac{4x}{(x^2+1)^2\frac{2|x|}{(x^2+1)}}\\
&=-\frac{2x}{|x|(x^2+1) }
\end{align}
Voila!
