复合函数求导y=x方乘以根号下x+根号x

Question

复合函数求导
y=x方乘以根号下x+根号x

Answer 1

y'=(x²)'*√(x+√x)+x²*[√(x+√x)]'
(x²)'=2x
[√(x+√x)]'
=1/{2[√(x+√x)]}*(x+√x)'
=1/{2[√(x+√x)]}*(1+1/2√x)
=(2√x+1)/{2[√(x+√x)]*2√x}
=(2√x+1)/[4√(x√x+x)]
所以y=2x√(x+√x)+(2x²√x+x²)/[4√(x√x+x)]