求下列函数的导数:(1)y=5x^2-4x+1 (2)y=(2x^2-1)(3x^2+1) (3)y=(x+cosx)/(x+sinx)
问题描述:
求下列函数的导数:(1)y=5x^2-4x+1 (2)y=(2x^2-1)(3x^2+1) (3)y=(x+cosx)/(x+sinx)
答
(1)y`=10x-4
(2)y`=4x(3x^2+1)+(2x^2-1)(6x)
=12x^3+4x+12x^3-6x
=24x^3-2x
(3)y`=[(1-sinx)(x+sinx)-(x+cosx)(1+cosx)]/(x+sinx)^2
=[sinx-xsinx-1-cosx-xcosx]/(x+sinx)^2
答
(1).y'=10x-4
(2).y=6x ^4-x^2-1 所以y'=24x^3-2x
(3).算不出来。。。。。
答
(1)y’=10x-4 :(2)y’=24x^3-2x :y’=(sinx-cosx-xsinx-xcosx-1)/(x+sinx)^2
答
1.y=10x-4
2.y=24x^3-2x
3.暂时没想到
答
1. y' = 10x - 42. y' = 4x(3x^2 - 1) + 6x(2x^2 - 1) = 24x^2 - 10x 3. y' = [(1-sinx)(x+sinx) - (1+cosx)(x+cosx)]/(x+sinx)^2 = (sinx - xsinx - cosx - xcosx - 1)/(x+sinx)^2