Given that y = f (INX), the second derivative of F (x) exists, find the second derivative of Y

Given that y = f (INX), the second derivative of F (x) exists, find the second derivative of Y

y=f(lnx)
that
y'=f '(lnx) *(lnx)'=1/x *f '(lnx)
The second derivative is obtained by further derivation
y"= -1/x^2 *f '(lnx) +1/x *f "(lnx) *(lnx)'
= -1/x^2 *f '(lnx) +1/x^2 *f "(lnx)