related rates

[dear2009]

Dear mathhelp participants,


Suppose that A, B, C are all time varying quantities, which at all times satisfy the equation:

(A^3) +(B)(C^5) = 1

Further suppose that at a particular instant,

A = 2,
B = 5, dB/dt= 3,
C = 2, dC/dt = 4.

Then dA/dt = ?

Thanks in advance

 

[arthur ohlsten]

A^3+BC^5=1 take derivative with respect to t
5A^4 dA/dt +B[5C^4]dC/dt+C^5 dB/dt=0

A=2
B=5 dB/dt=3
C=2 dC/dt=4

5[16] dA/dt + 5[5][16][4] +32[3]=0
80 dA/dt+1600+96=0
dA/dt=-[1696]/80
dA/dt=-21.2 answer

please check the math
Arthur