Question

Se considera functia f:(0,infinit) cu valori in R. f(x)=x^{2} lnx^{2} .
Aratati ca f'(x)=2x(2lnx+1), xapartine (0,infinit)

Answer 1

$\displaystyle f(x)=x^2\cdot \ln x^2=2x^2\cdot \ln x\\ f'(x)=2(x^2)'\cdot \ln x+2\cdot x^2\cdot (\ln x)'= 4x\cdot \ln x+2\cdot x^2\cdot \dfrac{1}{x}=\\ =4\cdot \ln x\cdot x+2\cdot x=\boxed{2x(2\ln x+1)}$