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