Assuming the validity of the operations on the r.h.s. find `dy/dt`
`y = 1 div [x +1 div (x +1 div (x +1 div ........))]`

Assuming the validity of the operations on the r.h.s. find dy/dt y = ln [ x + In (x + ln (x + ........))]

Assuming the validity of the operations on the r.h.s. find dy/dt y = sqrt[[sin x + sqrt{{sin x + sqrt((sin x + ........)}])}]

Find dy/dx e^(xy) + y sin x = 1

Find dy/dx xy^2 + x^2y + 1 = 0

Find dy/dx if y = x cot^(-1) (x/y)

If x^yy^x=1 , find dy/dx .

if y=e^(cos^(-1)x) then find dy/dx .

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

If x^y+y^x=1 , find dy/dx .