I got:
1/2t^(-1/2)(x+14) + SQRT of x.
why is this wrong?
I don't know why your derivative has a $\displaystyle t$ in it.
$\displaystyle y = x^{\frac{1}{2}}(x+14)$.
$\displaystyle \frac{dy}{dx} = x^{\frac{1}{2}}\,\frac{d}{dx}(x + 14) + (x + 14)\,\frac{d}{dx}(x^{\frac{1}{2}})$
$\displaystyle = x^{\frac{1}{2}} + \frac{1}{2}(x + 14)x^{-\frac{1}{2}}$
$\displaystyle = \sqrt{x} + \frac{x + 14}{2\sqrt{x}}$.