Limits Continuity And Differentiability

Let \(g(x) = {{{{(x - 1)}^n}} \over {\log {{\cos }^m}(x - 1)}};0 < x < 2,m\) and \(n\) are integers, \(m \ne 0,n > 0\), and let \(p\) be the left hand derivative of \(|x - 1|\) at \(x = 1\). If \(\mathop {\lim }\limits_{x \to {1^ + }} g(x) = p\), then