There is an alternative form for the definition of a derivative...$f'(a)=\lim_{x \rightarrow a} \frac{f(x)-f(a)}{x-a}$It is often used when your are analyzing a piecewise defined function where the continuity is questionable. If we re-write your problem to fit this form...$f'(5\pi)=\lim_{x \rightarrow 5\pi} \frac{f(x)-f(5\pi)}{x-5\pi}$If f(x) is the cosine...$f'(5\pi)=\lim_{x \rightarrow 5\pi} \frac{\cos (x)-\cos (5\pi)}{x-5\pi}$From this, it looks like f(x)=cos(x) and a=5pi .