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Find the derivative of f(x)=x^2log(2x)

Use the product rule (f'(x)=u'v+uv')

Let u=x2    =>    u'=2x

Let v=log(2x)  =>   v'=2/(2x)  =>    v'=1/x

Therefore f'(x)=2xlog(2x)+x2/x

f'(x)=2xlog(2x)+x

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