求导数及微分的算法

题目

求导数及微分的算法
y=cotx^1/2的导数算法,y=xsin2x的微分,y=arcsinx^1/2的微分,

答案

函数的导数和微分是有区别的!分部积分在这里是什么意思?(1)y'=-csc^2(x^(1/2))*(1/2)*(x^(-1/2))=-(1/2)(x^(-1/2))csc^2(x^(1/2)); (2)dy=[x'sin2x+x(sin2x)']dx=(sin2x+x*cos2x*2)dx=(sin2x+2xcos2x)dx; (3)dy=(-1/2){1/[(1-x)^(1/2)]}{1/[x^(1/2)]}dx=-1/{2[(x-x)^(1/2)]}dx.