If `y=tan^(-1)sqrt((x+1)/(x-1)),t h e n(dy)/(dx)i s` `(-1)/(2|x|sqrt(x^2-1))` (b) `(-1)/(2xsqrt(x^2-1))` `1/(2xsqrt(x^2-1))` (d) none of these

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

If y=(sqrt(a+x)-sqrt(a-x))/(sqrt(a+x)+sqrt(a-x)) ,then (dy)/(dx) is equal to (a) (a y)/(xsqrt(a^2-x^2)) (b) (a y)/(sqrt(a^2-x^2)) (c) (a y)/(xsqrt(a^2-x^2)) (d) none of these

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

If y=sqrt(log{sin((x^2)/3-1)}) , t h e n find (dy)/(dx)dot

int(sqrt(1-x^(2))-x)/(sqrt(1-x^(2))(1+xsqrt(1-x^(2))))dx is

int(x^4-1)/(x^2sqrt(x^4+x^2+1))dx= sqrt(x^2+1/(x^2)+1)+C (sqrt(x^4+x^2+1))/(x^2)+C (sqrt(x^4+x^2+1))/x+C (d) none of these

If y=sqrt((a-x)(x-b))- (a-b)tan^(-1)sqrt((a-x)/(x-b)),t h e nfin d(dy)/(dx)dot

If y=cos^(-1)((2x)/(1+x^2)),t h e n(dy)/(dx)i s (a) (-2)/(1+x^2) for all x (b) (-2)/(1+x^2) for all |x| 1 (d) none of these

If y=sqrt(logx+sqrt(logx+sqrt(logx+oo))),t h e n(dy)/(dx)i s (a) x/(2y-1) (b) x/(2y+1) (c) 1/(x(2y-1)) (d) 1/(x(1-2y))

int(x^(2)+1)/(xsqrt(x^(2)+2x-1)sqrt(1-x^(2)-x))dx is equal to