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Calculus Derivatives

  1. Oct 1, 2012 #1

    hsd

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    1. The problem statement, all variables and given/known data

    F(3)=−2, g(3)=9, f′(3)=−2, and g′(3)=2, find the following numbers:

    (a) (f+g)′(3)

    (b) (fg)′(3)

    (c) (f/g)′(3)

    (d) (f/(f−g))′(3)


    3. The attempt at a solution

    I already have (a) and (b) [a=0 and b=-22]

    for (c) i tried:

    (g(x)*f'(x) - f(x)g'(x)) / (g(x))^2

    evaluate at 3:
    (9)(-2) - (-2)(2) / 4
    -18 + 4 / 4
    -14/4
    -7/2

    WHICH IS THE WRONG ANSWER

    (d) I just cant get started.
     
  2. jcsd
  3. Oct 1, 2012 #2

    berkeman

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    Staff: Mentor

    The denominator for c should be g^2 and you plugged in g'^2 (simple error).
     
  4. Oct 1, 2012 #3

    berkeman

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    Staff: Mentor

    And for d), can you still just use the quotient rule? (I'm not sure, but try it...)
     
  5. Oct 1, 2012 #4

    Mark44

    Staff: Mentor

    Yes, use the quotient rule. After you get the derivative, evaluate the derivative at x = 3.
     
  6. Oct 1, 2012 #5

    hsd

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    I think I am applying the rule wrong. This is what I did:

    (f-g)'(f)-(f)'(f-g)/(f-g)
    [(-2)(-2)]'[-2]-[-2]'[(-2)(-9)]/[(-2)(-9)]
    8-22/-11
    -14/-11 (wrong answer)

    Can you please tell me what it is that I am doing wrong?
     
  7. Oct 2, 2012 #6

    Mark44

    Staff: Mentor

    You have three mistakes above:
    1. The terms in the numerator are switched, which will give you the wrong sign for your answer.
    2. The term in the denominator needs to be squared.
    3. You are missing a pair of parentheses in the numerator.
    It would be helpful if you included the arguments for the general derivative.
    Let h(x) = (f/g)(x), then h'(x) = (f/g)'(x) = [g(x)f'(x) - f(x)g'(x)]/g2(x)

    And then substitute 3 for x, similar to what I have done below.
    So h'(a) = [g(a)f'(a) - f(a)g'(a)]/g2(a)
     
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