" 18."y=sqrt((x^(2)+x+1)/(x^(2)-x+1))

If y=log sqrt((x^(2)+x+1)/(x^(2)-x+1))+(1)/(2sqrt(3)){tan^(-1)backslash(2x+1)/(sqrt(3))+tan^(-1)backslash(2x-1)/(sqrt(3))} then prove that (dy)/(dx)=(1)/(x^(4)+x^(2)+1)

if y=(sqrt(x^(2)+1)+sqrt(x^(2)-1))/(sqrt(x^(2)+1)-sqrt(x^(2)-1)), then (dy)/(dx) is

Simplify : (a) sqrt(y+sqrt(2xy-x^(2))) + sqrt(y-sqrt(2xy-x^(2))) (b) (x+sqrt(x^2-1))/(x-sqrt(x^(2)-1)) -(x-sqrt(x^(2)-1))/(x+sqrt(x^(2)-1))

If y=tan^(-1)sqrt((x+1)/(x-1)), then (dy)/(dx) is (-1)/(2|x|sqrt(x^(2)-1)) (b) (-1)/(2x sqrt(x^(2)-1))(1)/(2x sqrt(x^(2)-1))( d) none of these

If sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y), prove that (dy)/(dx)=sqrt((1-y^(2))/(1-x^(2)))

If sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y), prove that (dy)/(dx)=sqrt((1-y^(2))/(1-x^(2)))

If sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y) , then prove that (dy)/(dx)=sqrt((1-y^(2))/(1-x^(2)))

sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y), provethat (dy)/(dx)=sqrt((1-y^(2))/(1-x^(2)))

y=sqrt(1+x^(2)) and y'=(xy)/(1+x^(2))