What is the derivative of $ln(2x)$ ?

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Answer 1 · 2015-05-25T19:05:34

We can use the chain rule here, naming $u=2x$ and remembering that the chain rule states that

$(dy)/(dx)=(dy)/(du)(du)/(dx)$

So, now, for our function $ln(u)$ :

$(dy)/(du)=1/u$

And for the other part:

$(du)/(dx)=2$

Now, aggregating them:

$(dy)/(dx)=1/u*2=1/(cancel(2)x)*cancel2=color(green)(1/x)$

What is the derivative of ln(2x)ln(2x)?