设函数y=cosx+1,则dy=?这题纯粹是套入就行吗?dy=d(cosx+1)=-sinxdx ,怎么就得出了-sinxdx?
问题描述:
设函数y=cosx+1,则dy=?
这题纯粹是套入就行吗?dy=d(cosx+1)=-sinxdx ,怎么就得出了-sinxdx?
答
d/dx(cos x+1)
=d/dx(cosx)
=d/dx[sin (π/2-x)]
=d/du[sin (π/2-x)]×d/dx(π/2-x) (连锁律)
=cos (π/2-x)×(-1) (d/dx(sin x)=cos x)
=-cos (π/2-x)
=-sin x (cos (π/2-x)=sin x)
最后得出dcos x+1)=-sin xdx.