例6求y=x3-2x2+sinx的导数 解y=3x2-4x+cosx. 例7求y=x3nx的导数 解y=(x3lx (x3)y·lnx+x(lnx) 3x2·lnx+x 3x Inx+x Economic-mathematics 31-11 Wednesday, February 24 2021
Economic-mathematics 31 - 11 Wednesday, February 24, 2021 例6 2 sin . 求 y = x 3 − x 2 + x的导数 解 2 y = 3x − 4x 例7 ln . 求 y = x 3 x的导数 解 ( ln ) 3 y = x x + cos x. ( ) ln (ln ) 3 3 = x x + x x x x x x 1 3 ln 2 3 = + 2 2 = 3x ln x + x
例8求y=tanx的导数 解y=(tanx)’=( SInd cos d (sin x)'cos x-sin x(cos x) cos d 2 cosx x 2 sec d cos cos 即(tanx)'=sec2x. 同理可得(cotx)=-csc2x Economic-mathematics 31-12 Wednesday, February 24 2021
Economic-mathematics 31 - 12 Wednesday, February 24, 2021 例8 求 y = tan x的导数 . 解 ) cos sin = (tan ) = ( x x y x x x x x x 2 cos (sin ) cos − sin (cos ) = x x x 2 2 2 cos cos + sin = x x 2 2 sec cos 1 = = (tan ) sec . 2 即 x = x (cot ) csc . 2 同理可得 x = − x