Prove $f(x) = \sum_{n=1}^{\infty} \frac{x^n}{2^n} \cos{nx}$ is differentiable at $(-2, 2)$. Prove $$f(x) = \sum_{n=1}^{\infty} \frac{x^n}{2^n} \cos{nx}$$ is differentiable at $(-2, 2)$.
I can't use formula for radius of convergence, because it's not a power series ($x$ is present also in $\cos$).

HINT: Try to prove uniform convergence on $[-2+\alpha,2-\alpha]$ for any $0<\alpha<2$
