Question

What is the derivative of `x*x^(1/2)`?

Answer 1

`=3/2x^(1/2)`

Explanation:

`d/dx(x*x^(1/2))=d/dx(x^(1/2+1))=d/dx(x^(3/2))=3/2x^(3/2-1)=3/2x^(1/2)`

Answer 2

`d/(d x)(x*x^(1/2))=3/2*sqrt x`

Explanation:

`d/(d x)(x*x^(1/2))=d/(d x) (x)*x^(1/2)+d/(d x)(x^(1/2))*x`
`d/(d x)(x*x^(1/2))=1*x^(1/2)+1/2*(x^(1/2-1))*x`
`d/(d x)(x*x^(1/2))=x^(1/2)+1/2*x^(1/2)`
`d/(d x)(x*x^(1/2))=x^(1/2)(1+1/2)`
`d/(d x)(x*x^(1/2))=3/2*sqrt x`