If `y=sin^(-1)((1-x^(2))/(1+x^(2)))`,then `(dy)/(dx)=` a) `-(2)/(1+x^(2)),` b) `(2)/(2-x^(2)),` c) `(2)/(1+x^(2)),` d) `(1)/(2-x^(2))`

If y=sin^(-1)((1-x^2)/(1+x^2)) , then (dy)/(dx)= (a) -2/(1+x^2) (b) 2/(1+x^2) (c) 1/(2-x^2) (d) 2/(2-x^2)

If y=log((x^(2))/(e^(2))) then (d^(2)y)/(dx^(2)) equal to: a) -(1)/(x) b) -(1)/(x^(2)) c) (2)/(x^(2)) d) -(2)/(x^(2))

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

Solve: (dy)/(dx) + (2x)/(1+ x^(2)) y= (1)/((1+x^(2))^(2))

If y=(1+1/(x^2))/(1-1/(x^2)) , then (dy)/(dx) = a. -(4x)/((x^2-1)^2) b. -(4x)/(x^2-1) c. (1-x^2)/(4x) d. (4x)/(x^2-1)

If y=cos^2[tan^(-1)(sin[cot^(-1)x])], then (dy)/(dx) is (a) (-2x)/((x^2+2)^2) (b) (2x)/((x^2+2)^2) (c) 2/((x^2+2)^2) (d) (-2)/((x^2+2)^2)

If y=sin^(-1)x , show that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=0 .

If y=sin^(-1)((1-x^2)/(1+x^2))+cos^(-1)((1-x^2)/(1+x^2)) , find (dy)/(dx) .

If y= sin^(-1)((2x)/(x^(2)+1)) +sec^(-1)((1+x^(2))/(1-x^(2))) , prove that (dy)/(dx)=(4)/(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)))