Question

How do you use the formula (ln f(x))'= f'(x) / f(x) to show that lnx and ln(2x) have the same derivative?

Answer 1

We know that:

`(lnf(x))'=(f'(x))/f(x)`

So, for `lnx`, we see that `f(x)=x`, which implies that `f'(x)=1`.

Thus:

`(lnx)'=1/x`

For `ln(2x)`, we see that `f(x)=2x`, so `f'(x)=2`.

Thus:

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