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Math Help - derivatives

  1. #1
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    derivatives

    Hi,

    Q1.
    a) At what rate is the radius of a spherical balloon changing at the time that the radius is 10cm, if air is being pumped in at a rate of 40 cm^3 s^-1 ?

    b) Find an expression for dy/dx given that 3xy + e^y = 3.



    If there is anything unclear, let me know, thanks in advanced.
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  2. #2
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    Q1.
    a) At what rate is the radius of a spherical balloon changing at the time that the radius is 10cm, if air is being pumped in at a rate of 40 cm^3 s^-1 ?
    \frac{d}{dt}\left(V = \frac{4}{3}\pi r^3\right)

    \frac{dV}{dt} = 4\pi r^2 \cdot \frac{dr}{dt}

    you were given \frac{dV}{dt} and r ... solve for \frac{dr}{dt}


    b) Find an expression for dy/dx given that 3xy + e^y = 3.
    \frac{d}{dx}(3xy + e^y = 3)

    3x \cdot \frac{dy}{dx} + 3y + e^y \cdot \frac{dy}{dx} = 0

    solve for \frac{dy}{dx}
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