[f(x)=sin^(-1)((1+x^(2))/(2x))],[f(x)=cot^(-1)(2x-x^(2))]

f_(1)(x)=sin^(-1)(cos(sin^(2)x)),f_(2)(x)=cos^(-1)(sin(cos^(2)x)),f_(3)(x)=sin^(-1)(cos^(2)x)),f_(4)(x)=cos^(-1)(sin^(2)x)* Then which of the following is/are correct?

f (x) = sin ^(-1) ((1 + x ^(2))/( 2x )) is

f(x)=sin^(^^)(-1)[(1+x^(^^)2)/(2x)]' is

Find the domain of the following following functions: (a) f(x)=(sin^(-1))/(x) (b) f(x)=sin^(-1)(|x-1|-2) (c ) f(x)=cos^(-1)(1+3x+2x^(2)) (d ) f(x)=(sin^(-1)(x-3))/(sqrt(9-x^(2))) (e ) f(x)="cos"^(-1)((6-3x)/(4))+"cosec"^(-1)((x-1)/(2)) (f) f(x)=sqrt("sec"^(-1)((2-|x|)/(4)))

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

The range of f(x)=cot^(-1)(2x-x^(2)) is

The domain of f(x)=sin^(-1)((1+x^(2))/(2x)) is

Let f(x)=cot^(-1)((x^(2)-x+1)/(2x-3x^(2))+(x^(2)-x+1)/(3-2x)) and if f((3)/(2))+f((5)/(7))+f((2)/(3))+f((7)/(5))=k pi then k is

If f(x) = sin^(-1)(2x/(1+x^(2)) find f (x).