Bonjour Lolwlow
[tex]f (x)=\dfrac{1}{2} x^2\ln x\\\\f'(x)=\dfrac{1}{2}(x^2\ln x)'\\\\f'(x)=\dfrac{1}{2}[(x^2)'\times\ln x+x^2\times(\ln x)']\\\\f'(x)=\dfrac{1}{2}[2x\times\ln x+x^2\times\dfrac{1}{x}]\\\\f'(x)=\dfrac{1}{2}[2x\ln x+x]\\\\\boxed{f'(x)=x\ln x+\dfrac{x}{2}}[/tex]
