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Math Help - wacky derivative help

  1. #1
    Junior Member
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    wacky derivative help

    2 questions

    1. y = (x+(x+x^(1/2))^(1/2))^(1/2)
    y' = ?

    How do I do this?

    and another related question

    F(x) = f(xf(xf(x)))
    where f(1) = 2, f(2)=3, f'(1) = 4, f'(2) = 5, f'(3) = 6

    F'(1) = ?

    Help please!
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    Do you know the chain rule? Just apply the chain rule repeatedly. The final answer should be

    \frac{d}{dx}(f(x f(x f(x)))) = (x (x f'(x)+f(x)) f'(x f(x))+f(x f(x))) f'(x f(x f(x))).

    I won't do it by hand but you can look here for a complete answer (click "show steps"). Don't just copy the answer - make sure you understand the chain rule, it's important - you'll really have trouble later on if you don't master it now.

    Your first question is similar.
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