Answer
$\ln ^{2}x+2\ln x$
Work Step by Step
$\dfrac {d}{dx}\left( x\ln ^{2}x\right) =\left( \dfrac {d}{dx}\left( x\right) \right) \times \ln ^{2}x+\left( \dfrac {d}{dx}\left( \ln ^{2}x\right) \right) \times x=\ln ^{2}x+2\ln x\times \left( \dfrac {d}{dx}\left( \ln x\right) \right) \times x=\ln ^{2}x+2\ln x\times \dfrac {1}{x}\times x=\ln ^{2}x+2\ln x$
