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Math Help - Finding derivative of a function

  1. #1
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    Finding derivative of a function

    Hello,

    I'm supposed to find the derivative of the following.

    (4/3)Pi (r)^3

    Using the form (d/dx)f(x), or turning F(x) into F'(x) (Prime).

    Anyway, I'm supposed to solve r=2/3 but I'm not sure how I'm supposed to turn this function into F'(x).

    I think I'm supposed to do something like

    (4/3)Pi (3r)^2

    But I'm not sure how I should be applying the exponent when r = 2/3 - or whether I'm on the right track in that case.

    Any tips?

    Cheers
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  2. #2
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    Re: Finding derivative of a function

    Quote Originally Posted by astuart View Post
    Hello,

    I'm supposed to find the derivative of the following.

    (4/3)Pi (r)^3

    Using the form (d/dx)f(x), or turning F(x) into F'(x) (Prime).

    Anyway, I'm supposed to solve(?) r=2/3 <-- this equation is already solved
    but I'm not sure how I'm supposed to turn this function into F'(x).

    I think I'm supposed to do something like

    (4/3)Pi (3r)^2

    But I'm not sure how I should be applying the exponent when r = 2/3 - or whether I'm on the right track in that case.

    Any tips?

    Cheers
    What you posted is the term to calculate the volume of a sphere:

    V(r)=\frac43 \pi r^3

    Then V'(r)=\frac{dV}{dr}= \frac43 \pi r^2 \cdot 3=4 \pi r^2=A_s(r)

    which is the equation to determine the surface area of a sphere.

    To evaluate the volume or the surface area of a sphere with r = \frac23 you only have to plug in this value into these equations
    Thanks from astuart
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  3. #3
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    Re: Finding derivative of a function

    Quote Originally Posted by earboth View Post
    What you posted is the term to calculate the volume of a sphere:

    V(r)=\frac43 \pi r^3

    Then V'(r)=\frac{dV}{dr}= \frac43 \pi r^2 \cdot 3=4 \pi r^2=A_s(r)

    which is the equation to determine the surface area of a sphere.

    To evaluate the volume or the surface area of a sphere with r = \frac23 you only have to plug in this value into these equations
    I knew it was the volume of a sphere but I just wasn't sure how to put that into V'.

    Apparently the answer is (16(pi)/9)cm^3/cm - I'm just not sure how to get that answer...
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  4. #4
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    Re: Finding derivative of a function

    Quote Originally Posted by astuart View Post
    I knew it was the volume of a sphere but I just wasn't sure how to put that into V'.

    Apparently the answer is (16(pi)/9)cm^3/cm - I'm just not sure how to get that answer...
    V'(r) = 4\pi r^2

    V'\left(\frac{2}{3}\right) = 4 \pi \left(\frac{2}{3}\right)^2 = \, ?
    Thanks from astuart
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  5. #5
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    Re: Finding derivative of a function

    Quote Originally Posted by skeeter View Post
    V'(r) = 4\pi r^2

    V'\left(\frac{2}{3}\right) = 4 \pi \left(\frac{2}{3}\right)^2 = \, ?
    Ah, great, thanks for the help guys! I wasn't sure whether the Pi was considered a constant, and therefore can be excluded from the V' function, or whether a different rule applies for 'special' constants such as Pi.

    4/3 * 3/1 = 4 to get that section, then -1 from the exponent.

    (2/3)^2 = 4/9

    4/9 * 4/1 = 16(Pi)/9

    Thanks again, the Pi threw me off..
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