if `x=(1+lnt)/t^2` and `y=(3+2lnt)/t` then show that `y(dy)/(dx)=2x((dy)/(dx))^2+1`

If x = (1+logt)/t^2, y = (3+2logt)/t, t > 0 , prove that y(dy/dx) - 2x(dy/dx)^2 = 1

If x = (1 - t^2)/(1 + t^2) and y = (2t)/(1+t^2) , then show that (dy/dx) + x/y =0

If x^(2)+y^(2)=t+(1)/(t) and x^(4)+y^(4)=t^(2)+(1)/(t^(2)) then show that (dy)/(dx)=-(y)/(x) .

A function is reprersented parametrically by the equations x=(1+t)/(t^3); y=3/(2t^2)+2/t then the value of |(dy)/(dx)-x((dy)/(dx))^3| is__________

A function is reprersented parametrically by the equations x=(1+t)/(t^3); y=3/(2t^2)+2/t then the value of (dy)/(dx)-x((dy)/(dx))^3 is__________

If x=(1-t^2)/(1+t^2) and y=(2t)/(1+t^2) ,then (dy)/(dx)=

If x=(1-t^2)/(1+t^2) and y=(2t)/(1+t^2) ,then (dy)/(dx)=

If x=(1-t^2)/(1+t^2) and y=(2t)/(1+t^2) , prove that dy/dx+x/y=0

If x=(1-t^2)/(1+t^2) and y=(2at)/(1+t^2) , then (dy)/(dx)=