Calculus I

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  • #13257

    Ezra Halleck
    Participant

    2. 3.5: and are two differentiable functions satisfying and . Which of the following formulas represents ?
    A) B) etc

    #16788

    V. Panov
    Participant

    I can’t decide between A or D
    For A if you actually use f(0)=0 and g(0)=1
    the derivative (f/g)”(0) will always end up as 0/1 which is 0, even if you take the third, fourth, fifth derivative etc.

    For D the formula makes sense to me as well.

    I’m still leaning more towards A, not sure though.

    #16831

    Jenny P.
    Member

    I think its A cause no matter how many times you take the derivative it still should be 0..

    #16839

    Devindra
    Participant

    The way I did it I got E as my answer.

    (F/G)”(0) (f’g-g’f / g^2)
    U=F’g-g’F
    U’=F”g + g’f’ – g”f – g’f’
    = f”g- g”f

    U’-v-v’u / v^2

    (f”g-g”f)g^2 – (2gg’)(f’g-g’f) / g^4

    f”(0)-2f'(0)g'(0)

    #16842

    Ezra Halleck
    Participant

    The important thing to remember for this problem is that you can’t evaluate at 0 until you have finished taking the 2nd derivative. Devindra’s solution is more or less correct (actually more than less).
    1. He interchanges upper case and lower, probably because MS Word autochanges the first letter to upper case when you start a sentence.
    2. U’-v-v’u / v^2 should be u’v-v’u / v^2
    3. He fails to mention that v=g^2.

    #16844

    H Pardon
    Member

    OK so the first derivative is
    (g)(f’)-(f)(g’)/g^2

    #16872

    Dom
    Member

    You forgot the 2, I agree with Dev on this one

    #16877

    Dom
    Member

    I hope this helps a little

    #17055

    B Amarsingh
    Participant

    that actually helped me out, thx. and i ended up getting the correct answer

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