a) \({y'} = 3{\ln ^2}x + \left( {3x - 2} \right).{{2\ln x} \over x} = 3{\ln ^2}x + {{2\left( {3x - 2} \right)\ln x} \over x}\).
b) \({y'} = {x \over {\sqrt {{x^2} + 1} }}.\ln {x^2} + \sqrt {{x^2} + 1} .{{2x} \over {{x^2}}} = {{x\ln {x^2}} \over {\sqrt {{x^2} + 1} }} + {{2\sqrt {{x^2} + 1} } \over x}\).
c) \({y'} = \ln {1 \over {1 + x}} + x.{{ - {1 \over {{{\left( {1 + x} \right)}^2}}}} \over {{1 \over {1 + x}}}} = - \ln \left( {1 + x} \right) - {x \over {x + 1}}\).
d) \({y'} = {{{{2x} \over {{x^2} + 1}}.x - \ln \left( {{x^2} + 1} \right)} \over {{x^2}}} = {{2} \over {{x^2} + 1}} - {{\ln \left( {{x^2} + 1} \right)} \over {{x^2}}}\).
