Why Does the Chain Rule Apply Differently to the Derivative of (x^2+x)^(1/2)?

[nameVoid]

D= (x^2+x)^(1/2)

Why does the chain rule in this case produce D' = (1/2)(x^2+x)^(-1/2) (2x+1)(x')

and not D' = (1/2)(x^2+x)^(-1/2) (2x+1)(2x')

 

[rock.freak667]

$$\frac{dD}{dt}=\frac{dx}{dt} \times \frac{dD}{dx}$$

So like in the other thread, can you understand why now?