求下列函数的导数
(1) y=(2x²+3)(3x-1)
y=(2x²+3)(3x-1)=6x³-2x²+9x-3,故y′=18x²-4x+9
(2) y=√(x-2)²
y=√(x-2)²=︱x-2︱
当x≧2时,y=x-2,此时y′=1；当x≦2时,y=-(x-2)=-x+2,此时y′=-1.
(3) y=x-sin(x/2)cos(x/2)
y′=x′-{[sin(x/2)]′cos(x/2)+sin(x/2)[cos(x/2)]′}
=1-{[cos(x/2)](x/2)′cos(x/2)+sin(x/2)[-sin(x/2)](x/2)′}
=1-[(1/2)cos²(x/2)-(1/2)sin²(x/2)]=1-(1/2)[cos²(x/2)-sin²(x/2)]=1-(1/2)cosx
注“为什么(3x)'=3?”是因为(3x)′=3′x+3x′=0×x+3×1=3
常量的导数=0,即c′=0,3是常量,故3′=0；(xⁿ)′=nxⁿֿ¹.