" 9."y=sin^(-1)[(sqrt(1+x)-sqrt(1-x))/(2)]

If y=tan^(-1) [(sqrt(1+sinx)-sqrt(1-sin x))/(sqrt(1+sin x)+sqrt(1-sin x)]] where 0 lt x lt pi/2 find (dy)/(dx)

Find (dy)/(dx) , if y=sin^-1((sqrt(1+x)+sqrt(1-x))/2), -1ltxlt1

Prove the following: sin^-1x-sin^-1y = sin^-1[x(sqrt(1-y^2))-y(sqrt(1-x^2))]

Find (dy)/(dx), if y=sin^(-1)[x sqrt(1-x)-sqrt(x)sqrt(1-x^(2))]

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