<s>[INST] 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.
 [/INST] Use that $(1+x^2)^2\sqrt{1-\frac{(1-x^2)^2}{(1+x^2)^2}}=(1+x^2)\sqrt{(1+x^2)^2-\frac{(1+x^2)^2(1-x^2)^2}{(1+x^2)^2}}=(1+x^2)\sqrt{((1+x^2)+(1-x^2))((1+x^2)-(1-x^2))}=(1+x^2)\sqrt{2\cdot2x^2}$
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