Задание

\[\text{Найти}\ \ f'(x),\ \ \text{если}\ \ \ f(x) = 2^x\cdot{log_2{x}}.\]

\[f'(x) = 2^x(ln2\cdot log_2{x}+\frac{1}{xln2})\]

\[f'(x) = 2^x(ln2\cdot log_2{x}+\frac{1}{ln2})\]

\[f'(x) = 2^xln2\cdot log_2{x}+\frac{1}{xln2}\]

\[f'(x) = \frac{2^x}{x}\]