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Differentiating

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    In a question I was doing, the volume of a cylinder, V, was equal to

    (pi)r2h.

    I was also told the area was 4000 (so (pi)r2 = 4000). I substituted this value in and got V=4000h (I then went on to differentiate by calculating dV/dh)..

    If I was not given the value of the area, would it be possible to differentiate (pi)r2h ?
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    (Original post by sabre2th1)
    In a question I was doing, the volume of a cylinder, V, was equal to

    (pi)r2h.

    I was also told the area was 4000 (so (pi)r2 = 4000). I substituted this value in and got V=4000h (I then went on to differentiate by calculating dV/dh)..

    If I was not given the value of the area, would it be possible to differentiate (pi)r2h ?
    Well given that the area is a fixed constant of unknown quantity and you're still differentiating with respect to h you'd just get \dfrac{dV}{dh} = \pi r^2

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