If `f(x)=sin^(-1)((sqrt(3))/2x-1/2sqrt(1-x^2)),-1/2lt=xlt=1,t h e nf(x)` is equal to

If x in[-1/2,1] then sin^(-1)(sqrt(3)/(2)x-1/2sqrt(1-x^(2)))

If int(2x-sqrt(sin^(-1)x))/(sqrt(1-x^(2)))dx=C-2sqrt(1-x^(2))-(2)/(3)sqrt(f(x)) then f(x) is equal to

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

int sin^(-1)x cos^(-1)xdx=f^(-1)(x)[(pi)/(2)x-xf^(-1)(x)-2sqrt(1-x^(2))]+2x+c, then f(x) is equal to

If f(x)=(sin^(-1)x)/(sqrt(1-x^(2))),then(1-x^(2))f'(x)-xf(x)=

If f(x)=2sin^(-1)sqrt(1-x)+sin^(-1)(2sqrt(x(1-x))) , where x in (0,1/2),t h e nf^(prime)(x) is (a)2/(sqrt(x(1-x))) (b) zero (c)-2/(sqrt(x(1-x))) (d) pi

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

int_(-1)^(1)(x)/(sqrt(1-x^(2)))*sin^(-1)(2x sqrt(1-x^(2)))dx is equal to