The derivative of the function y = ln(ln(ln(x))) is calculated using the chain rule. The correct notation for the derivative is dy/dx, not ∂y/∂x, as the latter refers to partial derivatives. The initial assumption that the derivative is 1/x is incorrect; instead, the derivative requires multiple applications of the chain rule to account for the composite nature of the function.
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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.