y=f(sin^2(3x))求一阶二阶导数,

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y=f(sin^2(3x))求一阶二阶导数,

y=f(sin^2(3x))求一阶二阶导数,
y=f(sin^2(3x))求一阶二阶导数,

y=f(sin^2(3x))求一阶二阶导数,
解析
sin²3x'=2sin3xsin3x'
=6sin3xcos3x
6sin3xcos3x'=18cos²3x-18sin²3x
所以二阶导数18(cos²3x-sin²3x)f(sin²3x)

y=f(sin^2(3x))
y'=f'(sin^2(3x))(2sin(3x)cos(3x)(3)=3sin(6x)f'(sin^2(3x))
y''=9sin^2(6x)f''(sin^2(3x))+18cos(6x)f'(sin^2(3x))