Question

How do you find the derivative of `log_2 (x)`?

Answer 1

By changing its base and solving it then, as follows:

By `log` properties, we know that `(log_ab)=(logb/loga)`

Thus,

`log_2x=logx/log2`

Now, to derivate it, we must remember that there is no need to use the quotient rule, as the denominator can be understood as a constant (there's no variable in `log2`, it's just a number you can calculate promptly).

Thus,

`(dy)/(dx)=(1/x)/log2`

`(dy)/(dx)=color(green)(1/(xlog2))`