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Math Help - Derivatives

  1. #1
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    Derivatives

    Suppose that we have two functions, f(x) and g (x), and that
    • f (3) = 4,
    • g (3) = 5,
    • f '(3) = -4, and
    • g '(3) = 5.
    Calculate the values of the following derivatives when x is equal to 3.

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  2. #2
    Moo
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    Hello,

    Use the quotient rule..

    But I don't see any g function here oO

    So the derivative of f(x)/x : [x*f'(x)-f(x)]/x^2

    Since f(3) is known, f'(3) is known and x=3, you can easily calculate it
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  3. #3
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    Hello, Merdiemae!

    Suppose that we have a function, f(x), and that: . f(3) = 4,\;\;f'(3) = \text{-}4

    Calculate the value of \frac{d}{dx}\left(\frac{f(x)}{x}\right) when x = 3
    We need the Quotient Rule . . .

    . . \frac{d}{dx}\left(\frac{f(x)}{x}\right) \;=\;\frac{x\!\cdot\!f'(x) - 1\!\cdot\!f(x)}{x^2}


    Then: . \frac{d}{dx}\left(\frac{f(x)}{x}\right)\bigg]_{x=3} \;=\; \frac{3\!\cdot\!f'(3) - 1\!\cdot\!f(3)}{3^2} \;=\;\frac{3(\text{-}4) - 1(4)}{3^2} \;=\;\boxed{-\frac{16}{9}}

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