问题
解答题
求下列函数的导数
(1)y=2xtanx
(2)y=(x-2)3(3x+1)2.
答案
(1)∵y=2xtanx=2x
,∴y′=sinx cosx
=2×(sinx+xcosx)cosx-2xsinx(-sinx) cos2x
.2sinxcosx+2x cos2x
(2)y′=3(x-2)2(3x+1)2+2×3×(3x+1)(x-2)3=3(x-2)2(3x+1)(5x-3).
求下列函数的导数
(1)y=2xtanx
(2)y=(x-2)3(3x+1)2.
(1)∵y=2xtanx=2x
,∴y′=sinx cosx
=2×(sinx+xcosx)cosx-2xsinx(-sinx) cos2x
.2sinxcosx+2x cos2x
(2)y′=3(x-2)2(3x+1)2+2×3×(3x+1)(x-2)3=3(x-2)2(3x+1)(5x-3).