Question

Differentiate Functions of Other Bases In Exercise, find the derivative of the function.

Answer 1

Answer:

The derivative of the function is:

$g'(x) = \frac{1}{1.6094x}$

Step-by-step explanation:

If we have a function in the following format:

$g(x) = \log_{a}{f(x)}$

This function has the following derivative

$g'(x) = \frac{f'(x)}{f(x)*\ln{a}}$

In this problem, we have that:

$g(x) = \log_{5}{x}$

So $f(x) = x, f'(x) = 1, a = 5$

The derivative is

$g'(x) = \frac{f'(x)}{f(x)*\ln{a}}$

$g'(x) = \frac{1}{x*\ln{5}}$

$g'(x) = \frac{1}{1.6094x}$