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Math Help - [SOLVED] Derivative help

  1. #1
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    [SOLVED] Derivative help

    i need to find the derivative of 4/sqrt (x)
    Any help?
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    Quote Originally Posted by rawkstar View Post
    i need to find the derivative of 4/sqrt (x)
    Any help?
    4x^{-\frac{1}{2}}

    Can be differentiated using the standard method
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  3. #3
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    i'm just beginning my calc class so i dont know what that means
    can someone help me find the derivative using the limit of the definition
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    Quote Originally Posted by rawkstar View Post
    i'm just beginning my calc class so i dont know what that means
    can someone help me find the derivative using the limit of the definition
    Can you do algebra? Can you simplify the following?
    \frac{{\frac{4}{{\sqrt {x + h} }} - \frac{4}{{\sqrt x }}}}{h}
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    Quote Originally Posted by Plato View Post
    Can you do algebra? Can you simplify the following?
    \frac{{\frac{4}{{\sqrt {x + h} }} - \frac{4}{{\sqrt x }}}}{h}
    i know how to simplify the numerator
    my problem is that i don't know how to simplify the denominator
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  6. #6
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    Quote Originally Posted by rawkstar View Post
    i know how to simplify the numerator
    my problem is that i don't know how to simplify the denominator
    Did you get \frac{{\frac{4}{{\sqrt {x + h} }} - \frac{4}{{\sqrt x }}}}{h} = \frac{{4\sqrt x  - 4\sqrt {x + h} }}{{h\sqrt x \sqrt {x + h} }}?
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    no
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  8. #8
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    Quote Originally Posted by rawkstar View Post
    no
    Even so, do you understand how it was done? It is simple algebra.
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  9. #9
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    i'm not sure how you're going about this problem, this is what i'm doing
    ((4/sqrt(x+h)) - (4/(sqrt(x))) / h then
    (4 sqrt (x) - 4sqrt(x +h))/ (h)(x)(x + h) and im not sure where to go from here

    i do know simple algebra, i'm not stupid, im just trying to solve this problem the way me teacher is instructing me to
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  10. #10
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    Quote Originally Posted by rawkstar View Post
    i'm not sure how you're going about this problem, this is what i'm doing
    ((4/sqrt(x+h)) - (4/(sqrt(x))) / h then
    (4 sqrt (x) - 4sqrt(x +h))/ (h)(x)(x + h) and im not sure where to go from here
    i do know simple algebra, i'm not stupid, im just trying to solve this problem the way me teacher is instructing me to
    I have taught calculus courses off and on since 1964.
    The concepts of calculus in and of themselves are easy to understand.
    So what makes so hard for so many students?
    One simple fact: students with poor algebra skills donít get it.
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  11. #11
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    whatever, i solved it by myself
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  12. #12
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    Quote Originally Posted by Plato View Post
    Did you get \frac{{\frac{4}{{\sqrt {x + h} }} - \frac{4}{{\sqrt x }}}}{h} = \frac{{4\sqrt x  - 4\sqrt {x + h} }}{{h\sqrt x \sqrt {x + h} }}?

    Wow, I had this same exact problem for homework and I don't know how to do it either!!! xD

    Using the definition of a derivative method and not the power of the rule, you would then have to find the limit of the right side expression as it approaches h. If you plug in zero for h, you get 0 in the denominator. So what do you do from there since you can't factor?
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  13. #13
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    You can do it like this Power of One

    <br />
\frac{{4\sqrt x - 4\sqrt {x + h} }}{{h\sqrt x \sqrt {x + h} }}=4\frac{{\sqrt x - \sqrt {x + h} }}{{h\sqrt x \sqrt {x + h} }}\cdot \frac{\sqrt x + \sqrt {x + h}}{\sqrt x + \sqrt {x + h}} =<br />
4\frac{x-(x+h)}{h\sqrt x \sqrt {x + h}}\cdot\frac{1}{\sqrt x + \sqrt {x + h}}=<br />

    <br />
4\frac{-h}{h\sqrt x \sqrt {x + h}}\cdot\frac{1}{\sqrt x + \sqrt {x + h}}=<br />
\frac{-4}{(\sqrt x \sqrt {x + h})(\sqrt x + \sqrt {x + h})}<br />

    Now taking the limit

    <br />
\lim\limits_{h\to0}\frac{-4}{(\sqrt x \sqrt {x + h})(\sqrt x + \sqrt {x + h})}=\frac{-4}{x\cdot2\sqrt{x}}=\frac{-2}{x\sqrt{x}}<br />

    Hope that helps.
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  14. #14
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    Quote Originally Posted by hjortur View Post
    <br />
\frac{{4\sqrt x - 4\sqrt {x + h} }}{{h\sqrt x \sqrt {x + h} }}=4\frac{{\sqrt x - \sqrt {x + h} }}{{h\sqrt x \sqrt {x + h} }}\cdot \frac{\sqrt x + \sqrt {x + h}}{\sqrt x + \sqrt {x + h}} =<br />
4\frac{x-(x+h)}{h\sqrt x \sqrt {x + h}}\cdot\frac{1}{\sqrt x + \sqrt {x + h}}=<br />
    <br />
4\frac{-h}{h\sqrt x \sqrt {x + h}}\cdot\frac{1}{\sqrt x + \sqrt {x + h}}=<br />
\frac{-4}{(\sqrt x \sqrt {x + h})(\sqrt x + \sqrt {x + h})}<br />

    Now taking the limit

    <br />
\lim\limits_{h\to0}\frac{-4}{(\sqrt x \sqrt {x + h})(\sqrt x + \sqrt {x + h})}=\frac{-4}{x\cdot2\sqrt{x}}=\frac{-2}{x\sqrt{x}}<br />
    You are a spoilsport.
    Do you care if someone learns something?
    Or do you just want to show us what you can do?
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  15. #15
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    I am sorry if I have ruined this one. He was asking for help and sounded like he was stuck. In hindsight I probarbly should have just posted the first few steps.
    I am not a showoff, and am very sorry if I have come across as one.

    Should I edit the original post and remove the solution?
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