Can you solve the strange derivative of this complex function?

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    Derivative Strange
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Homework Help Overview

The discussion revolves around finding the derivative of a complex function defined by multiple nested square roots. The function is presented as f(x) = (x+(x+(x+(x+1)^.5)^.5)^.5)^.5), which suggests a challenging application of differentiation techniques.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of the chain rule as a method to differentiate the function, with one suggesting to repeatedly apply the chain rule to peel back the layers of the nested structure.

Discussion Status

Some participants have provided guidance on the use of the chain rule, indicating that it is a key approach for tackling the problem. However, there is a mix of reactions, with at least one participant expressing frustration about the complexity of the task.

Contextual Notes

The original poster indicates uncertainty about where to start, suggesting a potential lack of clarity in understanding the function's structure or the differentiation process. There may be an implied expectation of familiarity with differentiation techniques among participants.

thennigar
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here we go.
originally in root forum, like root under a root under a root etc... just don't know where to start with this one.

f(x) = (x+(x+(x+(x+1)^.5)^.5)^.5)^.5)
 
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You know the chain rule, right?...Now is the time to have lots of fun with it!
 
chain rule

Just keep applying the chain rule... over and over and over. Keep peeling back each layer until you reach the end:
f(x) = (x + g(x))^.5
f'(x) = .5(x + g(x))^(-.5) (1 + g'(x))
... etc...
 
That sucks. LOL.
 

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