Question

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

f(x) = log2 x

Answer 1

The derivative of the function is:

`f'(x) = (1)/(0.6931x)`

Explanation:

If we have a function in the following format:

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

This function has the following derivative

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

In this problem, we have that:

`f(x) = log_2(x)`

So
`g(x) = x, g'(x) = 1, a = 2`

The derivative is

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

`f'(x) = (1)/(x*ln(2))`

`f'(x) = (1)/(0.6931x)`