# Natural log (ln x) derivative question

1. Jan 2, 2013

### SteveM19

1. The problem statement, all variables and given/known data

This is to help out a 40something calc student -- thank you all in advance for your help

2. Relevant equations

If f (y) = ln ln ln x, what is ∂y/∂x?

3. The attempt at a solution

I came up with 1/x, which I got by applying ∂y/∂x ln x = 1/x three times, is this right? Thank you again for your help.

2. Jan 2, 2013

### BloodyFrozen

Is that a $f(y)$? Or like $f(x) = y =~ ...$

3. Jan 2, 2013

### SteveM19

I might have used the terminology incorrectly --

y = ln ln ln x

What is y prime?

4. Jan 2, 2013

### Staff: Mentor

As BloodyFrozen already noted, that should be f(x) = ...

Also, the problem should be asking for dy/dx, not ∂y/∂x, which is the partial derivative of y with respect to x. Unless I'm missing something, you want the ordinary derivative, dy/dx.
No, it's not right. You have a composite function, y = ln(ln(ln(x))), so you need to use the chain rule a couple of times. It also might be helpful to include parentheses as I did.

In response to your other question, you can take y' to be a synonym of dy/dx.