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 = 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 = sqrt[[sin x + sqrt{{sin x + sqrt((sin x + ........)}])}]

Find dy/dx x = y ln (xy)

Find dy/dx , when y = e^(x)ln x .

Find (dy)/(dx) when y = log|x| .

Find (dy)/(dx) if y = 10^(ln sinx)

Find dy/dx if y=log(sec x+tan x).

Find the derivative of log sin x w.r.t. x.

Find the second order derivative of log x.

Solve the following differential equations. x log x dy/dx +y=2 log x