Answer:
The derivative of the function is:
[tex]g'(x) = \frac{1}{1.6094x}[/tex]
Step-by-step explanation:
If we have a function in the following format:
[tex]g(x) = \log_{a}{f(x)}[/tex]
This function has the following derivative
[tex]g'(x) = \frac{f'(x)}{f(x)*\ln{a}}[/tex]
In this problem, we have that:
[tex]g(x) = \log_{5}{x}[/tex]
So [tex]f(x) = x, f'(x) = 1, a = 5[/tex]
The derivative is
[tex]g'(x) = \frac{f'(x)}{f(x)*\ln{a}}[/tex]
[tex]g'(x) = \frac{1}{x*\ln{5}}[/tex]
[tex]g'(x) = \frac{1}{1.6094x}[/tex]
