Respuesta :
Answer:
The derivative of the function is:
[tex]g'(x) = \frac{1}{2.0794*(2x - 5)}[/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]f(x) = \log_{8}{2x - 5}[/tex]
So [tex]f(x) = 2x - 5, f'(x) = 2, a = 8[/tex]
The derivative is
[tex]g'(x) = \frac{f'(x)}{f(x)*\ln{a}}[/tex]
[tex]g'(x) = \frac{1}{(2x-5)*\ln{8}}[/tex]
[tex]g'(x) = \frac{1}{2.0794*(2x - 5)}[/tex]
