I'm no expert,
if you have sqrt(u) you get 1/2sqrt(u)
I don't think you can do the chain rule because you have -8-sqrt(u),
so I think you have to take the derivative of -8 which is 0 - the derivative of sqrt(u).
Remember that you can split up [tex]\frac{d}{dx}\left(-8-\sqrt{x^{2}-4x+29}\right)[/tex] to get [tex]\frac{d}{dx}\left(-8\right)-\frac{d}{dx}\left(\sqrt{x^{2}-4x+29}\right)[/tex]. From there you can apply the chain rule.