[tex]( {ln}^{2} x - ln {x}^{2} + 1)'[/tex]
[tex] = ( {ln}^{2} x)' - (ln {x}^{2} )' + 1'[/tex]
[tex] = 2lnx \times (lnx)' - (2lnx)' + 0[/tex]
[tex] = 2lnx \times \frac{1}{x} - 2 \times (lnx)'[/tex]
[tex] = \frac{2lnx}{x} - 2 \times \frac{1}{x} [/tex]
[tex] = \frac{2lnx}{x} - \frac{2}{x} [/tex]
[tex] = \frac{2lnx - 2}{x} [/tex]
[tex] = \frac{2(lnx - 1)}{x} [/tex]
