Question

How do you find the derivative of `f(x) = log_x 2`?

Answer 1

Change the base: `log_x 2 = (ln2)/(lnx)`

Explanation:

`f(x) = log_x 2 = (ln2)/(lnx)`

I think maybe the quotient rule is clearest rather than rewriting any more.

`f'(x) = ((0)(lnx)-(ln2)(1/x))/(lnx)^2`

`= -ln2/(x(lnx)^2)`

If wished, we can rewrite again:

`= -(ln2)/lnx 1/(xlnx)`

`= -log_x 2/(xlnx)`