一條很難的數學問題,求解答

dz/dt = ∂z/∂x.dx/dt + ∂z/∂y.dy/dt
= 2xy^3dx/dt + 3x^2y^2dy/dt + 4dx/dt - 2ydy/dt + 3dy/dt
= (2xy^3+4)dx/dt + (3x^2y^2-2y+3)dy/dt
= (2*2*1^3+4)*0.6 + (3*2^2*1^2-2*1+3)*(-0.8)
= 4.8 - 11.2
= -6.4 dB/s

2013-05-31 18:39:26 補充：
Correction from the fourth line onwards:
= 4.8 - 10.4
= -5.6 dB/s

2013-06-01 10:40:00 補充：
Finding the rate of loudness change with respect to distance:

Unit vector of the direction <0.6, -0.8> (u) = <0.6, -0.8>/√(0.6^2+(-0.8)^2) = <0.6, -0.8>
Required rate
= (∂z/∂x+∂z/∂y)∙u
= (2*2*1^3+4)*0.6 + (3*2^2*1^2-2*1+3)*(-0.8)
= 8*0.6 + 13*(-0.8)
= 4.8 - 10.4
= -5.6 dB

The rate of loudness change should be with respect to distance, not with respect to time. There is no indication in the question regarding time.