(1)y=ln;
(2)y=log2(2x2+3x+1);
(3)y=esin(ax+b).
(1)y=ln;
(2)y=log2(2x2+3x+1);
(3)y=esin(ax+b).
解析:
(1)方法一:可看成y=lnu,u=
=
方法二:
=.
方法三:,
=
=.
(2)方法一:设y=log2u,u=2x2+3x+1,
则
=.
方法二:y′=[log2(2x2+3x+1)]′
=.
(3)方法一:设y=eu,u=sinv,v=ax+b,则yx′=yu′·
uv′·vx′=eu·cosv·a =acos(ax+b)·esin(ax+b).方法二:y′=[esin(ax+b)]′ =esin(ax+b)·
[sin(ax+b)]′=acos(ax+b)·esin(ax+b).