Question

How do you find the derivative for `ln(e^(2x))`?

Answer 1

Anna A. shows the "easy way" to answer this question, but it is often helpful to see other ways of answering a question.

What if you "messed up" and didn't simplify first?

No problem, you'll still get the correct answer.

We'll use `d/(dx)(ln(g(x))) = 1/g(x) g'(x)`

And, because, in this problem, `g(x)= e^(2x)`, we'll also use:
`d/(dx)(e^(2x)) = 2e^(2x)`

So, here we go:

`d/(dx)(ln(e^(2x))) = 1/e^(2x) [2e^(2x)] = (2e^(2x))/e^(2x)`,

but this answer simplifies to:

`d/(dx)(ln(e^(2x))) = (2e^(2x))/e^(2x) = 2`,

We got the same answer. We just took a different route to get there.