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Math Help - Please help, quick and simple question!

  1. #1
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    Please help, quick and simple question!

    hey everyone

    havin a bit of trouble with this,

    f(3) = -2
    f'(3) = 5

    find g'(3) if

    a. g(x) = 3x^2 - 5f(x)

    b. g(x) = (3x + 1) / f(x)

    i've tried differentiating it and subbing it in but no luck, thanks in advance.
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  2. #2
    Senior Member
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    Hi buddy.

    Quote Originally Posted by jimzer View Post
    hey everyone

    havin a bit of trouble with this,

    f(3) = -2
    f'(3) = 5

    find g'(3) if

    a. g(x) = 3x^2 - 5f(x)

    b. g(x) = (3x + 1) / f(x)

    i've tried differentiating it and subbing it in but no luck, thanks in advance.
    do you know this rule:

    g(x) = f(x) + h(x)+...

    => g'(x) = f'(x) + g'(x)+...

    Therefor

    a)  g(x) = 3x^2 - 5f(x)

    => g'(x) = (3x^2)' - 5 f'(x)

    g'(x) = 6x - 5f'(x)

    g'(3) = 6*3 - 5*f'(3)

    done

    b) Use the quotient rule, then you get

    g'(x) = \frac{(3x+1)' * f(x) - f'(x)*(3x+1)}{[f(x)]^2}

    = \frac{3*f(x) - f'(x) (3x+1)}{[f(x)]^2}

    Now x = 3

    ....

    Guess you can do it yourself, can't you?

    Yours,
    Rapha
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  3. #3
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    thanks a lot man, i've never been taught the g(x) = f(x) + h(x) rule before...

    if its not too much trouble can you explain to me what it is?

    you've been a huge help!! thanks and rep given!!
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  4. #4
    Member billa's Avatar
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    Quote Originally Posted by jimzer View Post
    thanks a lot man, i've never been taught the g(x) = f(x) + h(x) rule before...

    if its not too much trouble can you explain to me what it is?

    When you have a function, say g(x), that equals other functions added together

    g(x) = f(x) + h(x) + m(x) + j(x) ...

    then

    g'(x) = f'(x) + h'(x) + m'(x) + j'(x) ...

    This is from the addition rule of differentiation. There are other rules for multiplication, division, and multiplication by a constant. Here is a brief list of them: rules

    Hope that is what you meant.
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  5. #5
    Senior Member
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    Quote Originally Posted by jimzer View Post
    thanks a lot man, i've never been taught the g(x) = f(x) + h(x) rule before...

    if its not too much trouble can you explain to me what it is?
    I am sure you have seen the rule before.

    Wikipedia says: Sum rule in differentiation - Wikipedia, the free encyclopedia

    Best regards,
    Rapha
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