Can you solve the strange derivative of this complex function?

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The discussion revolves around solving the derivative of a complex nested function, f(x) = (x+(x+(x+(x+1)^.5)^.5)^.5)^.5. Participants emphasize the importance of applying the chain rule repeatedly to unravel the layers of the function. The process involves differentiating each nested component step by step, which can become tedious. A humorous acknowledgment of the difficulty in this task is shared among contributors. Ultimately, the discussion highlights the complexity of derivatives in multi-layered functions and the necessity of perseverance in calculus.
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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