Question

Just a few more steps to go on this one, not sure how the algebra goes after the first few steps.

derive y = arctan( x - sqrt ( 1+ x^2 ) )

y' = [ 1 / ( 1 + ( x - sqrt ( 1+x^2 ) ) ] * [ 1- (1/2)( 1+x^2 )^(-1/2) * 2x ]

y' = (1 - x( 1+x^2 )^(-1/2) ) / ( 1 + (x -( 1+x^2 )^(1/2) )

simplified answer is 1/(2 (1+x^2))

can't see how to get there... I have tried replacing (1+x^2) with a variable... can't seem to get anywhere.