y=xcosx2的导数怎么求?

y=xcosx2的导数怎么求?
2024-12-03 03:50:50
推荐回答(2个)
回答1:

积法则
(fg)'=f'g+fg'
链式
f(g(x))'=f'(g(x))*g'(x)

先求cos(x^2)的孙肢祥导数
显然对应的
f(x)=cosx
g(x)=x^2
f(g(x))'=f'(g(x))*g'(x)

=-sin(x^2)*2x
对于整体,则搏f(x)=x,g(x)=cos(x^2)
(fg)'饥郑=f'g+fg'

=1*cos(x^2)+x*[-sin(x^2)*2x]
=cos(x^2)-sin(x^2)*2x^2

回答2:

y=xcos(x~2)
y'宏州厅迹橘=x'蔽隐*cos(x~2)+x*[cos(x~2)]'
=cos(x~2)+x*[-sin(x~2)]*2x
=cos(x~2)-2(x~2)sin(x~2).