求复合函数的高阶导数Wearegivenafunctionf(x)=(x^2-3x+2)^(n)*cos(x^2),wherenisaconstant.Answerallpartsfrompart(a)topart(b):(a).whatisf(5)(x),the5th-orderderivativeoff(x)?(b).Doesthereexistageneralexpression

Question

求复合函数的高阶导数
We are given a function f(x) = (x^2 - 3x + 2)^(n) * cos(x^2),where n is a constant.Answer all parts from part (a) to part (b):
(a).what is f(5)(x),the 5th-order derivative of f(x)?
(b).Does there exist a general expression for f(n)(x),the n-th order derivative of f(x)?State your reasons clearly.
Thank you in advance.

Answer 1

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