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Math Help - [SOLVED] derivatives

  1. #1
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    [SOLVED] derivatives

    So the question is.. Find the gradient of the following curves at the given point.

    f(x) = 5 / (root x) at the point where x=9

    I know that Root x = x^1/2

    But the numerator being 5 has confused me... Where would I go from here?
    Thankyou for any help.
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  2. #2
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    Hello,
    Quote Originally Posted by Corko93 View Post
    So the question is.. Find the gradient of the following curves at the given point.

    f(x) = 5 / (root x) at the point where x=9

    I know that Root x = x^1/2

    But the numerator being 5 has confused me... Where would I go from here?
    Thankyou for any help.
    You have to find f'(9)

    The 5 is not disturbing. Because the derivative of af(x), where a is a constant is af'(x)

    So \left[\frac{5}{\sqrt{x}}\right]'=5 \cdot \left[\frac{1}{\sqrt{x}}\right]'

    Can you calculate this derivative ?
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  3. #3
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    So that would be 5x^1/2

    which differentates to 2.5x^-1/2 ?
    I think...

    P.S - I'm sorry I haven't learned the codes for correct displaying of the expression
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  4. #4
    Moo
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    Quote Originally Posted by Corko93 View Post
    So that would be 5x^1/2

    which differentates to 2.5x^-1/2 ?
    I think...

    P.S - I'm sorry I haven't learned the codes for correct displaying of the expression
    Nope, it's 5x^{-1/2} (click on the picture to get the code)

    So it differentiates to 5 \cdot \left(-\frac 12\right)  x^{-1/2-1}=-2.5 x^{-3/2}
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  5. #5
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    So when I substitute the x value back in to work out my gradient

    <br /> <br />
-2.5 (9)^{-3/2} = -0.092592596<br /> <br />

    Either I'm going wrong somewhere or I'm supposed to represent that as a surd?
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  6. #6
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    Quote Originally Posted by Corko93 View Post
    So when I substitute the x value back in to work out my gradient

    <br /> <br />
-2.5 (9)^{-3/2} = -0.092592596<br /> <br />

    Either I'm going wrong somewhere or I'm supposed to represent that as a surd?
    9^{-3/2}=\frac{1}{9^{3/2}}=\frac{1}{(9^{1/2})^3}=\frac{1}{3^3}=\frac{1}{27}
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  7. #7
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    Well that would explain alot!
    Thankyou Moo!
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