1.函数y=2sin 3x的导数是( )
A.2cos 3x B.-2cos 3x
C.6sin 3x D.6cos 3x
解析:y′=(2sin 3x)′=6cos 3x.
答案:D
2.y=(3x2+2x)5的导数是( )
A.5(3x2+2x)4(6x+2)
B.(6x+2)5
C.10(3x+2)4
D.5(3x+2)4(6x+2)
解析:y′=5(3x2+2x)4•(3x2+2x)′
=5(3x2+2x)4(6x+2).
答案:A
3.y=log3cos2x的导数是( )
A.y′=-2log3e•tan x ` B.y′=2log3e•cot x
C.y′=-2log3cos x D.y′=log3ecos2x
解析:y′=1cos2xlog3e•(cos2x)′=1cos2xlog3e•2cos x•(cos x)′=1cos2xlog3e•2cos x•(-sin x)=-2log3e•tan x,故选A.
答案:A
4.函数y=x2cos 2x的导数为( )
A.y′=2xcos 2x-x2sin 2x
B.y′=2xcos 2x-2x2sin 2x
C.y′=x2cos 2x-2xsin 2x
D.y′=2xcos 2x+2x2sin 2x
解析:y′=(x2)′cos 2x+x2(cos 2x)′=2xcos 2x+x2(-sin 2x)•(2x)′=2xcos 2x-2x2sin 2x.
答案:B