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.

Divide et impera.
Under the square root you have
$$
1-\frac{(1-x^2)^2}{(1+x^2)^2}=
\frac{(1+x^2)^2-(1-x^2)^2}{(1+x^2)^2}=\frac{4x^2}{(1+x^2)^2}
$$
so the big square root is actually
$$
\frac{2|x|}{1+x^2}
$$
Thus your formula becomes
$$
-\frac{4x}{(1+x^2)^2}\frac{1+x^2}{2|x|}=-\frac{2x}{|x|(1+x^2)}
$$
