Question

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

g(x) = log5 x

Answer 1

The derivative of the function is:

`g'(x) = (1)/(1.6094x)`

Explanation:

If we have a function in the following format:

`g(x) = log_a(f(x))`

This function has the following derivative

`g'(x) = (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) = (f'(x))/(f(x)*ln(a))`

`g'(x) = (1)/(x*ln(5))`

`g'(x) = (1)/(1.6094x)`