The discussion revolves around finding the derivative of the function y = ln(ln(ln(x))). Participants are exploring the correct interpretation of the function and the appropriate notation for derivatives.
The conversation is ongoing, with some participants providing clarifications regarding the function's notation and the derivative's notation. There is a recognition that the original poster's approach may not be correct due to the composite nature of the function, prompting further exploration of the chain rule.
There is a mention of potential confusion regarding the use of partial derivatives versus ordinary derivatives, indicating a need for clarity in the problem setup. Additionally, participants are encouraged to use parentheses for clarity in the function's expression.
BloodyFrozen said:Is that a ##f(y)##? Or like ##f(x) = y =~ ...##
As BloodyFrozen already noted, that should be f(x) = ...SteveM19 said:Homework Statement
This is to help out a 40something calc student -- thank you all in advance for your helpHomework Equations
If f (y) = ln ln ln x, what is ∂y/∂x?
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.SteveM19 said: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.