Let $f ( x ) , g ( x )$ be functions on the real line $\mathbb { R }$ such that both $f ( x ) + g ( x )$ and $f ( x ) g ( x )$ are differentiable. Which of the following is FALSE ?\\
(A) $f ( x ) ^ { 2 } + g ( x ) ^ { 2 }$ is necessarily differentiable.\\
(B) $f ( x )$ is differentiable if and only if $g ( x )$ is differentiable.\\
(C) $f ( x )$ and $g ( x )$ are necessarily continuous.\\
(D) If $f ( x ) > g ( x )$ for all $x \in \mathbb { R }$, then $f ( x )$ is differentiable.