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Math Help - Derivative Chain Rule Question.

  1. #1
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    Derivative Chain Rule Question.

    Newton's Law states the force (F) exerted by a point with mass M on another points of mass m is F=GmM/r^2

    Here G is a constant and r is the distance between the two points in meters. Let r be a function of time in seconds, where r(t) = 10^6sin( π t/300). (To clear confusion: r(t) equals to 10 to the power of 6 times sin( pi times t over 300))

    What is the rate that F is changing with respect to time when t = 50, G = 6.673 x 10^-11 Nm^2/kg^2, m=70kg, and M = 6x10^24 kg?

    Thank you for your time and help!
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    Re: Derivative Chain Rule Question.

    You have F = c*[1/r(t)]^2 = c * r(t)^(-2) where r(t) is a known function. What is the power rule for differentiation and can you use this?
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    Re: Derivative Chain Rule Question.

    F=GmM/r^2

    G = 6.673 x 10^-11 Nm^2/kg^2,
    m=70kg, and
    M = 6x10^24 kg?

    Then GmM is a constant in F=GmM/r^2
    Let GmM = c for simplicity

    F=cr^(-2)

    dF/dt = -2c(r^(-3)) * dr/dt ...chain rule

    r(t) = 10^6sin( π t/300)

    dr/dt = r'(t) = 10^6*(π/300)*cos( π t/300)

    Find r(5) and r'(5) by substituting t=5
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    Re: Derivative Chain Rule Question.

    Thank you guys for helping me out !
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