y=cos(x+3),大学的用定义求导?

y'
=lim (cos(x+△x+3) - cos(x+3) )/△x
=lim (cos(x+3)·cos△x - sin(x+3)·sin△x - cos(x+3) )/△x
=lim (cos(x+3)·(cos△x -1) )/△x - lim (sin(x+3)·sin△x )/△x
=lim (-△x²/2)cos(x+3)/△x - lim sin(x+3)·(sin△x /△x)
=lim -△x·cos(x+3)/2 - sin(x+3)·×1
=0- sin(x+3)
= -sin(x+3)