推论 (1)D∑f(x)=∑f(x (2)[C(x)=C(x); (3)[If(x)=f1(x)/2(x)…fn(x) +…+f1(x)f2(x)…fm(x) ∑∏f(x)/k(x) i=1k=1 k≠i (uvw)=uvw+uv'w+uvw
推论 (1) [ ( )] ( ); 1 1 = = = n i i n i fi x f x (2) [Cf (x)] = Cf (x); ( ) ( ); ( ) ( ) ( ) (3) [ ( )] ( ) ( ) ( ) 1 1 1 2 1 2 1 = + + = = = = n i n k i k i k n n n i i f x f x f x f x f x f x f x f x f x (uvw) = u v w+ uv w+ uvw
二、例题分析 例1求y=x3-2x2+sinx的导数 解y=3x2-4x+cosx 例2求y=sin2xlnx的导数 解y=2sinx·cosx·lnx y=2cos. x In x+2 sin x(sin x). Inx +sinx. cos x. =2 cos 2xInx+sin 2x
二、例题分析 例1 2 sin . 求 y = x 3 − x 2 + x的导数 解 2 y = 3x − 4x 例2 求 y = sin 2x ln x的导数 . 解 y = 2sin x cos x ln x y = 2cos x cos x ln x+ 2sin x (− sin x) ln x x x x 1 + 2sin cos + cos x. sin 2 . 1 2cos 2 ln x x = x x +