y=(x sin^(-1)x)/(sqrt(1-x^(2)))

y=sin^(-1)((x)/(sqrt(1+x^(2))))+cos^(-1)((1)/(sqrt(1+x^(2))))

Prove that tan^(-1)((1-x)/(1+x))-tan^(-1)((1-y)/(1+y))=sin^(-1)((y-x)/(sqrt(1+x^(2))*sqrt(1+y^(2))))

Find (dy)/(dx) in the following: y=sin^(-1)(2x sqrt(1-x^(2))),-(1)/(sqrt(2))

y = sin^(-1)(x/sqrt(1+x^2)) + cos^(-1)(1/sqrt(1+x^2))

Prove the following "tan"^(-1)((1-x)/(1+x))-"tan"^(-1)((1-y)/(1+y))="sin"^(-1)((y-x)/(sqrt(1+x^(2))sqrt(1+y^(2)))) .

If y=(sin x)^(x)+sin^(-1)sqrt(1-x^(2)) then find (dy)/(dx)