Question

f(x)= 1/x(1+lnx). Aratati ca f'(x)= ln(1+lnx)​

Answer 1

$f(x)= \ln(1+\ln x)\\ \\ f'(x) = \dfrac{(1+\ln x)'}{1+\ln x} = \dfrac{\dfrac{1}{x}}{1+\ln x} = \dfrac{1}{x(1+\ln x)}\quad \checkmark$