\(\displaystyle f^{(n)}(a), g^{(n)}(a)\) exists. Prove \(\displaystyle (f+g)^{(n)}(a) = f^{(n)}(a) + g^{(n)}(a)\). How do I even begin to start to prove or disprove this? The only thing I see in my book is that \(\displaystyle (f^n)'(c) = n(f(c))^{n-1}f'(c)\)