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Math Help - Differentiation Shortcuts and me

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    1

    Differentiation Shortcuts and me

    (2x^3-4x^2+3)/x^2
    Find f'(x)


    I do the following:

    Numerator:

    2x^3-4x^2+3
    6x^2-8x+3

    Denominator
    x^2
    2x

    so, (6x^2-8x+3)/2x is the f'(x) according to what I just did
    but the book says the answer is (2x^3-6)/(x^3)
    ????

    I'll post more of this nature that I screwed up if however you help me solve this won't suffice for the other, similar problems

    And,

    Let g(x) = 9f(x) and let f'(-6) = -6. Find g'(-6).

    I don't even know where to begin here.
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  2. #2
    Senior Member
    Joined
    Nov 2008
    Posts
    461
    Hi mate

    Quote Originally Posted by necroramo View Post
    (2x^3-4x^2+3)/x^2
    Find f'(x)


    I do the following:

    Numerator:

    2x^3-4x^2+3
    6x^2-8x+3
    Thats wrong.
    (+3)' = 0
    This term has no x in it!

    Quote Originally Posted by necroramo View Post
    Denominator
    x^2
    2x
    Thats Ok.
    Quote Originally Posted by necroramo View Post
    so, (6x^2-8x+3)/2x is the f'(x) according to what I just did
    but the book says the answer is (2x^3-6)/(x^3)
    ????
    You must use the Quotient rule
    <br />
\frac{(6x^2-8x)x^2-( 2x^3-4x^2+3)*2x}{(x^2)^2}

    =\frac{(6x^2-8x)x^2-( 2x^3-4x^2+3)*2x}{x^4}

    = \frac{(6x^2-8x)x^1-( 2x^3-4x^2+3)*2}{x^3}

    = \frac{6x^3-8x^2-4x^3+8x^2-6}{x^3}

    = \frac{6x^3-8x^2-4x^3+8x^2-6}{x^3}

    = \frac{2x^3-6}{x^3}

    = 2*\frac{(x^3-3)}{x^3}

    Quote Originally Posted by necroramo View Post
    I'll post more of this nature that I screwed up if however you help me solve this won't suffice for the other, similar problems

    And,

    Let g(x) = 9f(x) and let f'(-6) = -6. Find g'(-6).

    I don't even know where to begin here.
    I guess there are many solutions for this problem.
    One of them is very simple:

    f'(-6) = -6

    I guess f(x) = mx+b, you know f'(-6) = -6 = m

    => f(x) = -6x + b

    g(x) = 9f(x) = 9*(-6x+b) = -54x + 9b

    g'(x) = -54

    You just have to find a function with f'(-6) = -6, it isnt that hard, (then to findd the antiderivative) and multiply it with 9.
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