江画工太猩院 例2设函数f(x)=sm,求( sin x)'x(sin x)' 解( ( Sin x)=lim ch) sin(x sIn x h-0 sIn lim cos(r cos x h→0 即(sinx)y=cosx. sin x)T=cosx x 2江西理工大学理学院 例2 ( ) sin , (sin ) (sin ) . 4 π = = ′ ′ x 设函数 f x x 求 x 及 x 解 h x h x x h sin( ) sin (sin ) lim0 + − ′ = → 2 2 sin ) 2 limcos( 0 h h h x h = + ⋅ → = cos x. 即 (sin x)′ = cos x. 4 4 (sin ) cos π = π = ∴ ′ = x x x x . 2 2 =