Two spacecraft are following paths in space given by r₁ = (sin(t), t, 1²) and r₂ = (cos(t), 1-t, t³). If the temperature for the points is given by T(x, y, z) = x²y(5-z), use the Chain Rule to determine the rate of change of the difference D in the temperatures the two spacecraft experience at time t = 4.

Two spacecraft are following paths in space given by r₁ = (sin(t), t, 1²) and r₂ = (cos(t), 1-t, t³). If the temperature for the points is given by T(x, y, z) = x²y(5-z), use the Chain Rule to determine the rate of change of the difference D in the temperatures the two spacecraft experience at time t = 4.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter6: Applications Of The Derivative

Section6.3: Implicit Differentiation

Problem 44E

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