Question

What is the derivative of `f(x)= ln2x`?

Answer 1

`f'(x)=1/x`

Explanation:

According to the chain rule,

`d/dx[lnu]=1/u*u'`

Thus,

`d/dx[ln2x]=1/(2x)*d/dx[2x]`

`=1/(2x)*2=1/x`

Another way to think about this problem is to first split up the logarithm using logarithm rules:

`f(x)=ln2+lnx`

Thus, when differentiating, `ln2` is just a constant, so

`f'(x)=d/dx[lnx]=1/x`