(1)y=1/(a^2-x^2)^(1/2)
y'=(-1/2)[1/(a^2-x^2)^(3/2)](-2x)=x/(a^2-x^2)^(3/2).因此y'=(a-x)/(a^2-x^2)^(3/2)错了.
(2)y=[cos(1-2x)]^3
y'=3[cos(1-2x)]^2*[-sin(1-2x)](-2)=3cos(1-2x)*[2sin(1-2x)cos(1-2x)]=3cos(1-2x)sin2(1-2x).
y'=6[cos(1-2x)]^2*sin(1-2x)也正确.
(3)y=ln[x+(x^2+1)^(1/2)]
y'={1/[x+(x^2+1)^(1/2)]}*[1+(1/2)(2x)/(x^2+1)^(1/2)]
={1/[x+(x^2+1)^(1/2)]}*{[(x^2+1)^(1/2)+x]/(x^2+1)^(1/2)}
=1/(x^2+1)^(1/2).因此y'=(2x^2+1)/x*(x^2+1)^(1/2)+x^2+1错了.
(4)y=lnsin1/2(a-π/4)
y'=[1/sin1/2(a-π/4)]cos1/2(a-π/4)(1/2)=1/2cot1/2(a-π/4);
若y=lnsin(1/2*a-π/4),
则y'=[1/sin(1/2*a-π/4)]cos(1/2*a-π/4)(1/2)=1/2cot((1/2*a-π/4).这题要看清1/2是否在小括号内.