The derivative of $\cos^{-1}(2x^2-1)$ w.r.t $\cos^{-1}x$ is

Question

$$\begin{array}{1 1}(A)\;2 & (B)\;\frac{-1}{2\sqrt{1-x^2}}\\(C)\;\frac{2}{x} & (D)\;1-x^2\end{array}$$