標題:

derivative!! 10pts!!!

發問:

If A,B,C are functions of time related by A^2 = B^3 C^4, and B(7)=3 , C(7) =2 , A'(7) =5, and C'(-4), find B'(7).

最佳解答:

A2 = B3C4 [A(7)]2 = [B(7)]3[C(7)]4 = (3)3(2)4 = 432 A(7) = +- 12sqrt3 Differentiate both sides with respect to t 2AA' = 3B2B'C4 + 4B3C3C' Put t = 7, If A(7) = 12sqrt3, B'(7) = 8 + (5/18)sqrt3 If A(7) = -12sqrt3, B'(7) = 8 - (5/18)sqrt3

 

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