※ 引述《ChenYM (老宅男一個)》之銘言：
: 朋友問的
: 但我搞不定，所以上來請教前輩高手們
: Suppose that g is the inverse function of a
: differentiable function f and F(x)=g(g(x)).
: If f(4)=3 ,g(4)=5,f'(4)=0.5 and f'(5)=2
: , then F'(3)=?
f(4) = 3 => g(3) = 4
f(x) = y, g(y) = x
f(g(x)) = x => 1 = f'(g(x))g'(x)
g'(x) = [f'(g(x))]^(-1)
g'(3) = [f'(g(3))]^(-1) = [f'(4)]^(-1) = 2
g'(4) = [f'(g(4))]^(-1) = [f'(5)]^(-1) = 1/2
F'(3) = g'(u)| g'(3)
u=g(3)
= g'(4) g'(3)
= (1/2)(2) = 1
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