Big$-$O Theorems

If $d(n)$ is $O(f(n))$ and $e(n)$ is $O(g(n))$ show that:

$d(n)+e(n)$ is $O(f(n)+g(n))$

$d(n)e(n)$ is $O(f(n)g(n))$

If $d(n)$ is $O(f(n))$ : Is this true?

$2^{d(n)}$ is $O(2^{f(n)})$