求4sin(3x)cos(x)的导数式如题
问题描述：
求4sin(3x)cos(x)的导数式
如题
答
4sin(3x)'cosx+4sin(3x)*(cosx)'
=4cos(3x)*3*cosx+4sin(3x)*(-sinx)
=12cos(3x)cosx-4sin(3x)sinx
答
=4*(3*cos(3x))*cos(x)+4*sin(3x)(-sin(x))
=12cos(3x)cos(x)-4sin(3x)sin(x)
答
同意楼上的
答
4{cos(3x)3cosx+sin(3x)(-sin(x))}=12cos(3x)cosx-4sinxsin(3x)
答
12cos(3x)cos(x)-4sin(3x)sin(x)
答
求导公式：(uv)'=u'v+v'u
复合函数求导公式：[f(g(x))]'=f'(g(x))g'(x)
[4sin(3x)cos(x)]'
=[4sin(3x)]'cos(x)+4sin(3x)[cos(x)]'
=4cos(3x)×(3x)'×cos(x)+4sin(3x)(-sin(x))
=12cos(3x)cos(x)-4sin(3x)sin(x)
答
4sin(3x)cos(x)的导数式为
4(cos(3x)cos(x)*3-sin(3x)sin(x))=12cos(x)cos(3x)-4sin(3x)sin(x)