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Answer 1 · 2017-04-10T20:09:45

#d/dx (lnx)^2 = (2lnx)/x#

#d^2/dx^2 (lnx)^2 = (2 -2 lnx )/x^2#

Using the chain rule:

#d/dx (lnx)^2 = (2lnx)( d/dx lnx )= (2lnx)/x#

Then:

#d^2/dx^2 (lnx)^2 = d/dx ((2lnx)/x) = 2 d/dx(lnx/x)#

and using the quotient rule:

#d^2/dx^2 (lnx)^2 = 2 (x d/dxlnx - lnx d/dx x)/x^2#

#d^2/dx^2 (lnx)^2 = 2 (x *1/x - lnx )/x^2#

#d^2/dx^2 (lnx)^2 = 2 (1 - lnx )/x^2#