求函数的导数:(1)y=1⼀(a^2-x^2)^(1⼀2) ------参考答案为x⼀(a^2-x^2)^(3⼀2),

(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。

求函数的导数:(1)y=1/(a^2-x^2)^(1/2) ------参考答案为x/(a^2-x^2)^(3/2),我的答案为(a-x)/(a^2-x^2)^(3/2);
(2)y=[cos(1-2x)]^3-------参考答案为3cos(1-2x)sin2(1-2x),我的答案为6[cos(1-2x)]^2*sin(1-2x);
(3)y=ln[x+(x^2+1)^(1/2)]------参考答案为1/(1+x^2)^(1/2),我的答案为(2x^2+1)/x*(x^2+1)^(1/2)+x^2+1;
(4)y=lnsin1/2(a-pi/4)-----参考答案为1/2cot(1/2*a-pi/4),我的答案为1/2cot1/2(a-pi/4) ,请大家帮忙分析下是谁错了?谢谢.

(1)y=1/(a^2-x^2)^(1/2)
Y’=-1/2(a^2-x^2)^(-3/2)*(-2x)=x(a^2-x^2)^(-3/2)=x/(a^2-x^2)^(3/2)
答案正确
(2)y=[cos(1-2x)]^3
Y’=3[cos(1-2x)]^2*(-sin(1-2x))*(-2)=6 sin(1-2x)[cos(1-2x)]^2=3cos(1-2x)sin2(1-2x)
都正确
(3)y=ln[x+(x^2+1)^(1/2)]
y’=[1+1/2*2x/(x^2+1)^(1/2)]/[x+(x^2+1)^(1/2)]
=[1+x/(x^2+1)^(1/2)]/[x+(x^2+1)^(1/2)]
=1/(1+x^2)^(1/2)
答案正确
(4)y=lnsin1/2(a-pi/4)
y’=1/sin[1/2(a-pi/4)]*cos((a-pi/4)/2)*1/2=1/2*cot[(a-pi/4)/2]
你正确

a^2这是代表什么？a的2次方吗？