##d/dxln(lnx)=1/(lnx)*1/x=1/(xlnx)##

Derivative of ln x is 1/x, ie ##d/dx lnx=1/x## Derivative of the ln of a function is 1 over the function, multiplied by the derivative of the function So ##d/dxln(lnx)=1/(lnx)*1/x=1/(xlnx)##