Question

求下图函数的导数？

Answer 1

y
=( x^2+1)/√x
=x^(3/2) + x^(-1/2)
y' = (3/2)x^(1/2) -(1/2)x^(-3/2)

追问

能详细点吗？

能详细点吗？

追答

y
=( x^2+1)/√x
=( x^2+1).x^(-1/2)
=x^(3/2) + x^(-1/2)
y'
= (3/2)x^(3/2-1) -(1/2)x^(-1/2-1)
=(3/2)x^(1/2) -(1/2)x^(-3/2)

追问

我用除法公式怎么算出来不一样？

追答

那是一样！
y=( x^2+1)/√x
y'
=[√x.(2x) - ( x^2+1)/(2√x) ]/x
=[2√x.(2x) - ( x^2+1)/√x ]/(2x)
=[ 3x^(3/2) - x^(-1/2) ]/(2x)
=(3/2)x^(1/2) - (1/2)x^(-3/2)

追问

谢谢！我可算找出问题了