So to find the 1st derivative I use the Chain Rule:$\displaystyle y = (5x - 1)^{\frac{1}{2}}$

$\displaystyle y' = \frac{1}{2}(5x - 1)^{\frac{1}{2} - 1} \cdot (5 - 0) \\

= \frac{5}{2}(5x - 1)^{-\frac{1}{2}}$

2nd:

Multiplication rule [f'(x)*g(x) + f(x)*g'(x)] and Chain Rule:

$\displaystyle y'' = \frac{5}{2}(5x - 1)^{-\frac{1}{2}} \\

= 0\cdot (5x - 1)^{-\frac{1}{2}} + \frac{5}{2}\cdot [-\frac{1}{2}(5x - 1)^{-\frac{1}{2} - 1} \cdot (5 - 0)] \\

= \frac{5}{2}\cdot (-\frac{5}{2})(5x - 1)^{-\frac{3}{2}} \\

= -\frac{25}{4}(5x - 1)^{-\frac{3}{2}}$

3rd:

Multiplication rule [f'(x)*g(x) + f(x)*g'(x)] and Chain Rule:

$\displaystyle y''' = -\frac{25}{4}(5x - 1)^{-\frac{3}{2}} \\

= 0\cdot (5x - 1)^{-\frac{3}{2}} + -\frac{25}{4}\cdot [(-\frac{3}{2}(5x - 1)^{-\frac{3}{2}-1}) \cdot (5 - 0)] \\

= -\frac{25}{4}\cdot (-\frac{15}{2})(5x - 1)^{-\frac{5}{2}} \\

= \frac{375}{8}(5x - 1)^{-\frac{5}{2}} \\

= \frac{375}{8(5x-1)^{\frac{5}{2}}}$

I think I got this one wrong but this is how I worked it out...have I done any step incorrectly here?