求函数的导数①y＝x(x平方＋x分之1＋x的三次方分之1)②y＝(根号x加1)(根号x分之1减1)

Question

求函数的导数
①y＝x(x平方＋x分之1＋x的三次方分之1)
②y＝(根号x加1)(根号x分之1减1)

Answer 1

①y＝x(x平方＋x分之1＋x的三次方分之1)
y=x(x^2+1/x+1/x^3)
y=x^3+1+1/x^2
y=x^3+1+x^(-2)
y'=3x^2+0+(-2)x^(-2-1)
y'=3x^2-2/x^3
②y＝(根号x加1)(根号x分之1减1) x>0
y=（根号x+1)(1/根号x-1)
y=1-根号x+1/根号x-1
y=-x^(1/2)+x^(-1/2)
y'=-1/2x^(1/2-1) + (-1/2)x^(-1/2-1)
y'=-1/2[x^(-1/2)+x^(-3/2)]
y'=-1/2x^(-1/2)[1+1/x]
y'=-1/2(根号x) * (1/x+1/x^2)