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Math Help - Help me to derivate!

  1. #1
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    Help me to derivate!

    I've tried to derivate this function a couple of times but since I'm not very into all the rules I'm afraid I did it incorrect.

    Will anyone tell me if this is right:

    f(x)= (1/3)(pi)((xR/2pi)^2)((R^2)-((xR/2pi)^2))^0.5)

    f'(x)= 1/3 * pi * (xR/2pi)^2
    = (1/3)(pi)(2)(xR/2pi)(1/2pi)
    = (1/3)(xR/2pi)
    = xR/6pi


    I'm sorry if it looks messy!

    Thanks,
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  2. #2
    Junior Member
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    Do you mean;

    1/3 \pi \left( \frac{xR}{2 \pi} \right)^{2} (R^{2}- \sqrt( \left( \frac{xR}{2 \pi} \right)^{2}))

    is
    1/3 \pi \left( \frac{xR}{2 \pi} \right)^{2} (R^{2}-  \left( \frac{xR}{2 \pi} \right) )
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  3. #3
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by ninjajulez View Post
    I've tried to derivate this function a couple of times but since I'm not very into all the rules I'm afraid I did it incorrect.

    Will anyone tell me if this is right:

    f(x)= (1/3)(pi)((xR/2pi)^2)((R^2)-((xR/2pi)^2))^0.5)

    f'(x)= 1/3 * pi * (xR/2pi)^2
    = (1/3)(pi)(2)(xR/2pi)(1/2pi)
    = (1/3)(xR/2pi)
    = xR/6pi


    I'm sorry if it looks messy!

    Thanks,
    f(x)= \frac{\pi}{3} \left(\frac{xR}{2\pi}\right)^2 \left(R^2-\left(\frac{xR}{2\pi}\right)^2\right)^{\frac{1}{2}  }


    f(x)= \frac{\pi}{3} \cdot \frac{x^2R^2}{4\pi ^2} \cdot \left(R^2 - \frac{x^2R^2}{4\pi ^2} \right)^{\frac{1}{2}}

    f'(x)=\frac{\pi}{3} \left(\frac{2xR^2}{4\pi ^2} \cdot \left(R^2 - \frac{x^2R^2}{4\pi ^2} \right)^{\frac{1}{2}}+\frac{x^2R^2}{4\pi ^2} \cdot\frac{1}{2} \left(\frac{-2xR^2}{4\pi ^2}\right)\cdot \left(R^2 - \frac{x^2R^2}{4\pi ^2} \right)^{\frac{-1}{2}} \right)

    I used this

    f(x) = g(x) \cdot h(x)

    f'(x) = g'(x) \cdot h(x) + g(x) \cdot h'(x)
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