Compute the derivative of the function

$f(x)=\sqrt[\phantom{2}]{\frac{x^{2}1}{x^2-1}}$

Select one:

a$.-(\frac{x^{2}1}{x^2-1}{)}^{-\frac{1}{2}}$

b$.(\frac{x^{2}1}{x^2-1}{)}^{-\frac{1}{2}}\frac{2x^3}{(x^2-1{)}^2}$

c$.-(\frac{x^{2}1}{x^2-1}{)}^{-\frac{1}{2}}*\frac{2x}{(x^2-1{)}^2}$

d$.-(\frac{x^{2}1}{x^2-1}{)}^{\frac{1}{2}}\frac{2x}{(x^2-1{)}^2}$