Question

if y=sec^-1(x+1/x-1) + sin^-1(x-1/x+1), x>0. find dy/dx

Answer 1

d/dxsin^-1(x-1/x+1)
suppose (x-1/x+1) is p
and
d/dxsin^-1x=1/$\sqrt{1-x^2}$
so
d/dxsin^-1p
1/$\sqrt{1-p^2}$ *d/dxp
substituting the value of p
[x+1]/$2\sqrt{x}$*d/dx x-1/x+1
x+1/$2\sqrt{x}$*[(x+1)*1-(x-1)*1]/(x+1)^2
1/$(x+1) \sqrt{x}$