Question

急急急。。。数学求导数题（x+(x+x^1/2)^1/2)1/2) 真的不会啊，麻烦数学好的帮帮忙！！

比较急，答对加分！！！

Answer 1

用求复合函数导数的法则：
设y=[x+(x+x^1/2)^1/2]^1/2,
则y'=1/{2[x+(x+x^1/2)^1/2]^1/2}*{1+1/[2(x+x^1/2)^1/2]*[1+1/(2x^1/2)]}
=1/{2[x+(x+x^1/2)^1/2]^1/2}*{1+[2x^1/2+1]/[4x^1/2*(x+x^1/2)]}
=[4x^1/2*(x+x^1/2)+2x^1/2+1]/{8x^1/2*(x+x^1/2)*[x+(x+x^1/2)^1/2]^1/2}.

Answer 2

f’（x）=0.5（x+（x+x^0.5）^0.5）^（-0.5）*（1+0.5（x+x^0.5）^（-0.5））*（1+0.5x^（-0.5））

Answer 3

0.5*（x+（x+x^0.5)^0.5)^(-0.5)*(1+(1+0.5x^(-0.5))*(0.5*(x+x^0.5)^(-0.5)))

Answer 4

1啊