If `y=f(x)+(1)/(y)`, then `(dy)/(dx)=(y^(2)f'(x))/(1+y^(2))`

A: If y = x ^(y) then (dy)/(dx) = (y ^(2))/(x(1- log y )) If y = f (x) ^(y), then (dy)/(dx) = (y ^(2) f '(x))/(f (x) [1- ylog f (x)])= (y ^(2) f'(x))/(f (x) [1- log y])

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

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

A : If y = sqrt( sinx + y ) then (dy)/(dx) = (cos x )/( 2y -1) R: If y = sqrt(f(x) + y) then (dy)/(dx) = (f'(x))/(2y -1).

Express the following differential equation in the form f(x)dx+g(y)dy=0 . (dy)/(dx)=(1+y^(2))/(1+x^(2))

Let y=f (x) and x/y (dy)/(dx) =(3x ^(2)-y)/(2y-x^(2)),f(1)=1 then the possible value of 1/3 f(3) equals :

Let y=f (x) and x/y (dy)/(dx) =(3x ^(2)-y)/(2y-x^(2)),f(1)=1 then the possible value of 1/3 f(3) equals :

If y=f(cosx)" and "f'(x)=cos^(-1)x," then "(dy)/(dx)=

Solve the following differential equations (i) (1+y^(2))dx = (tan^(-1)y - x)dy (ii) (x+2y^(3))(dy)/(dx) = y (x-(1)/(y))(dy)/(dx) + y^(2) = 0 (iv) (dy)/(dx)(x^(2)y^(3)+xy) = 1