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A function \( f: R \rightarrow R \) satisfies the equation \( f(x+y)=f(x) f(y) \) for all \( x, y \in R \) and \( f(x) \neq 0 \) for all \( x \in R \). If \( f(x) \) is differentiable at \( x=0 \) and \( f^{\prime}(0)=2 \), then \( f^{\prime}(x) \)
(A) \( f(x) \)
(B) \( -f(x) \)
(C) \( 2 f(x) \)
(D) none of these
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