Natural log (ln x) derivative question

[SteveM19]

Homework Statement

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

Homework Equations

If f (y) = ln ln ln x, what is ∂y/∂x?

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.

 

[BloodyFrozen]

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

 

[SteveM19]

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

I might have used the terminology incorrectly --

y = ln ln ln x

What is y prime?

 

[Mark44]

Homework Statement

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

Homework Equations

If f (y) = ln ln ln x, what is ∂y/∂x?

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.

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.

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.