Simple derivative problem

[DinosaurEgg]

Here is the equation and my attempt on a dry-erase board:

My steps are similar to the textbook's up until I hit that 3x^1/2. Why is it disappearing with their method? It's late at night and my brain is fried; I have a feeling this will be painfully obvious to me in the morning, but in case it isn't, perhaps someone can fill me in on what I missed?

 

[Ray Vickson]

Here is the equation and my attempt on a dry-erase board:

My steps are similar to the textbook's up until I hit that 3x^1/2. Why is it disappearing with their method? It's late at night and my brain is fried; I have a feeling this will be painfully obvious to me in the morning, but in case it isn't, perhaps someone can fill me in on what I missed?

Recall that $1/\sqrt{x} = x^{-1/2},$ so
$$\frac{d}{dx} \frac{2x-1}{\sqrt{x}} = x^{-1/2}\frac{d}{dx} (2x-1) + (2x-1) \frac{d}{dx} x^{-1/2}.$$
You had written $(d/dx) x^{1/2}.$

RGV