Re: [微積] f(x)=g(x+h(x^3)) f'(x)=?

[susanyen (蘇珊)]

※ 引述《AngelBeats01 (Angel-Beats)》之銘言：
: f(x)=g(x+h(x^3))
: f'(X)=?
: 最近重溫微積分想不太出這題解法　
: 想請問這題如何解　感謝!

f(x)=g(x+h(x^3))

chain rule ==> f(x)=p(q(x)) , f'(x)=p'(q(x))*q'(x)

f'(x)=g'(x+h(x^3))*[x+h(x^3)]'
     =g'(x+h(x^3))*{1+[h(x^3)]'}
     =g'(x+h(x^3))*{1+h'(x^3)*(x^3)'}
     =g'(x+h(x^3))*[1+h'(x^3)*(3x^2)]

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