calculus
posted by daria on .
Find the second derivative of y=loge(logex)
Show that y=loge(logex) is a solution of the equation
xd^2y/dx^2 + x(dy/dx)^2 + dy/dx=o

The first derivative of ln (ln x) is dy/dx = 1/(x*ln x)
The second derivative is:
d^2y/dx^2 = [ln x/x^2  (1/x^2)]/(ln x)^2
= 1/(x^2 ln x) 1/(x ln x)^2
x d^2y/dx^2 = 1/(x ln x)  (1/x)/lnx^2
It seems to fit the differential equation