How to calculate $\lim_{x \to 0}\frac{\sqrt[3]{\cos x}-\sqrt{\cos x}}{x^2}$
Compute: $\lim_{x\to 0}\frac{\sqrt[m]{\cos(\alpha x)}-\sqrt[n]{\cos{(\beta x)}}}{x^2},\;m,n\in\mathbb N,\alpha,\beta\in\mathbb R$