Question

What is `dy/dx` of `2xsqrtx`?

Answer 1

`dy/dx=3sqrtx`

Explanation:

`y=2xsqrtx=uv`

`dy/dx=u(dv)/dx+v(du)/dx`

`u=2x`
`(du)/dx)=2`

`v=sqrtx=x^(1/2)`
`(dv)/(dx)=1/2*x^(1/2-1)=x^(-1/2)/2`

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