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d/dx [arc sen v] = ( dv/dx)/ raiz de [1-v^2]
Para tu caso v=2/x
Entonces tienes
d/dx [arc sen (2/x)] = d/dx(2/x) / raiz de [1-(2/x)^2]
d/dx [arc sen (2/x)] = -2/(x^2) / raiz de [1-(2/x)^2]
simplificando esto te da
d/dx [arc sen (2/x)] = - 2 / [x raiz de ( x^2 - 4)]