y=f(sin^2(3x))求一阶二阶导数,要详细些,谢谢啦

2025-06-23 05:31:24
推荐回答(2个)
回答1:

解析

sin²3x'=2sin3xsin3x'
=6sin3xcos3x

6sin3xcos3x'=18cos²3x-18sin²3x

所以二阶导数18(cos²3x-sin²3x)f(sin²3x)

回答2:

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))