Answer:
The derivative of the function is:
[tex]f'(x) = \frac{1}{0.6931x}[/tex]
Step-by-step explanation:
If we have a function in the following format:
[tex]f(x) = \log_{a}{g(x)}[/tex]
This function has the following derivative
[tex]f'(x) = \frac{g'(x)}{g(x)*\ln{a}}[/tex]
In this problem, we have that:
[tex]f(x) = \log_{2}{x}[/tex]
So [tex]g(x) = x, g'(x) = 1, a = 2[/tex]
The derivative is
[tex]f'(x) = \frac{g'(x)}{g(x)*\ln{a}}[/tex]
[tex]f'(x) = \frac{1}{x*\ln{2}}[/tex]
[tex]f'(x) = \frac{1}{0.6931x}[/tex]
