[x+(x+x^0.5)^0.5]^0.5 的导数? 复合函数的求导就是觉得怪怪的_数学解答

[x+(x+x^0.5)^0.5]^0.5 的导数? 复合函数的求导就是觉得怪怪的

人气：491 ℃　时间：2020-05-09 06:49:18

解答

导数=0.5*[x+(x+x^0.5)^0.5]^(-0.5)*[x+(x+x^0.5)^0.5]'
=0.5*[x+(x+x^0.5)^0.5]^(-0.5)*[1+0.5*(x+x^0.5)^(-0.5)*(x+x^0.5)']
=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)]