※ 引述《saskuran (beyourguard)》之銘言:
: https://i.imgur.com/puPsgLL.jpg
: 15題,求解如何把合成函數
: 分解成多個單一的函數
: 謝謝
h(v) = v [1 + v^2]^(1/3)
w(v)= v
k(u) = [u]^(1/3)
g(v) = 1 + v^2
h(v) = w(v) k(g(v))
h' = w'(v) k(g(v)) + w(v) k(g(v))'
= 1 k(g(v)) + v dk/dg dg/dv
= [1 + v^2]^(1/3) + v (1/3)[g(v)]^(-2/3) * 2v
= [1 + v^2]^(1/3) + v (1/3)[1 + v^2]^(-2/3) * 2v
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