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Math Help - Derivitives

  1. #1
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    Derivitives

    Find f '(a).

    f(x) = \frac{1}{\sqrt{x+6}}

    plugging this into the formula i get

    <br />
\lim_{h \to 0} \frac{\frac{1}{\sqrt{x+h+6}}-\frac{1}{\sqrt{x+6}}}{h}

    which simplified all the way down to

    \lim_{h \to 0} \frac{-h}{h(\sqrt{x+h+6})(\sqrt{x+6})(\sqrt{x+6}+\sqrt{x+  h+6})}




    then to

    \lim_{h \to 0} \frac{-1}{(\sqrt{x+h+6})(\sqrt{x+6})(\sqrt{x+6}+\sqrt{x+h  +g})}

    and finally

    \lim_{h \to 0} \frac{-1}{(x+6)^2}


    but...its wrong

    any help?




    EDIT: or would the final answer be

    \lim_{h \to 0} \frac{-1}{(x+6)(\sqrt{x+6}+\sqrt{x+6}})
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by silencecloak View Post
    Find f '(a).

    f(x) = \frac{1}{\sqrt{x+6}}

    plugging this into the formula i get

    <br />
\lim_{h \to 0} \frac{\frac{1}{\sqrt{x+h+6}}-\frac{1}{\sqrt{x+6}}}{h}

    which simplified all the way down to

    \lim_{h \to 0} \frac{-h}{h(\sqrt{x+h+6})(\sqrt{x+6})(\sqrt{x+6}+\sqrt{x+  h+6})}

    then to

    \lim_{h \to 0} \frac{-1}{(\sqrt{x+h+6})(\sqrt{x+6})(\sqrt{x+6}+\sqrt{x+h  +6})}
    Correct !

    and finally

    \lim_{h \to 0} \frac{-1}{(x+6)^2}


    but...its wrong

    any help?
    I see where the problem is

    When substituting h=0, we get :
    \frac{-1}{(\sqrt{x+6})(\sqrt{x+6})(\sqrt{x+6} {\color{red}+} \sqrt{x+6})}

    (\sqrt{x+6})(\sqrt{x+6})=x+6, you got it right !

    But \sqrt{x+6} {\color{red}+} \sqrt{x+6}={\color{red}2} \sqrt{x+6}

    Got it ?
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  3. #3
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    Quote Originally Posted by Moo View Post
    Hello,

    Correct !


    I see where the problem is

    When substituting h=0, we get :
    \frac{-1}{(\sqrt{x+6})(\sqrt{x+6})(\sqrt{x+6} {\color{red}+} \sqrt{x+6})}

    (\sqrt{x+6})(\sqrt{x+6})=x+6, you got it right !

    But \sqrt{x+6} {\color{red}+} \sqrt{x+6}={\color{red}2} \sqrt{x+6}

    Got it ?
    darn algebra, so easy to get mixed up

    so i end up with


    <br /> <br />
\lim_{h \to 0} \frac{-1}{(x+6)(2\sqrt{x+6})}<br />

    ah, but since its for f'(a), do i now need to replace the x with a?
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  4. #4
    Moo
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    Quote Originally Posted by silencecloak View Post
    darn algebra, so easy to get mixed up

    so i end up with


    <br /> <br />
\lim_{h \to 0} \frac{-1}{(x+6)(2\sqrt{x+6})}<br />

    ah, but since its for f'(a), do i now need to replace the x with a?
    Yes =)
    And it is correct now !
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  5. #5
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    awesome


    thank you very much, as usual!
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