[tex]\it f(x) = x\log_2x
\\\;\\
f' (x) = (x\log_2x)' = x'\log_2x + x (\log_2x)' =1\cdot\log_2x +x\cdot\dfrac{1}{x}\cdot \dfrac{1}{ \ln2} =
\\\;\\ \\\;\\
= \log_2x + \dfrac{1}{\ln2} = \dfrac{ \ln x}{ \ln2} +\dfrac{1}{\ln 2} = \dfrac{\ln x +1}{\ln2} = \dfrac{1+\ln x}{\ln2}[/tex]
