Find the limit of: x3^(x) / 3^(x) - 1 as x goes to 0.
When you take L'Hospital's Rule, how do you take the derivative of the top?

Question

Find the limit of: x3^(x) / 3^(x) - 1  as x goes to 0.
When you take L'Hospital's Rule, how do you take the derivative of the top?

anonymous · Answer

when you use L'Hospital's rule*, sorry typo.

zepdrix · Answer

So the top is the product rule yes? :)

Do you remember how to take the derivative of any exponential term (one without e as the base)?

anonymous · Answer

so x*((3^(x)) (ln(3) + 3^(x) * x for the top?

zepdrix · Answer

I think you didn't take the derivative of anything on that second term :O

anonymous · Answer

* 1 at the end, sorry. I put X.

zepdrix · Answer

Oh yes looks good :) hehe

anonymous · Answer

Yeah, sorry.

anonymous · Answer

You have to apply the multiplication rule. That would be:
$$(x)\prime . 3^x + x . (3^x)\prime$$

anonymous · Answer

ahaha xD

anonymous · Answer

The book confused me, I saw x3^(x) and I didn't know what to do. But as soon as you said product rule, I knew what to do. Thank you very much, both of you =)