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Problem 41 Hard Difficulty

If $ f( x) = x^2/ (1 + x), $ find $ f" (1). $

Answer

$=\frac{1}{4}$

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Video Transcript

hands clear. So when you right here, so we have a pup. Acts is equal to x square over one plus X. We're gonna difference she using the quotient rule to find the first year of it to get one plus x d over d X for X square minus x square d over DX for one plus x. This becomes equal to all over one plus square. This becomes equal to one plus x times two x minus X square times one over one plus x square just equal to two x plus x square over one plus x square. We're gonna find the second derivative Using the closure role, we get one plus x square D over DX go to X plus X square minus two X plus x square Do you over d x one plus x square all over one plus X square needs. Square that again and this becomes equal to one plus x times two plus two x minus two times two X plus x square all over one plus x cute. We just have to plug in X is equal to one. Then we get, uh, off. The second derivative of one is equal to 14 Yeah,