Let \( f: \mathbb{R} \rightarrow \mathbb{R} \) be a differentiable ...

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Let \( f: \mathbb{R} \rightarrow \mathbb{R} \) be a differentiable function with \( f(0)=1 \) and satisfying the equation
\[
f(\mathrm{x}+\mathrm{y})=f(\mathrm{x}) f^{\prime}(\mathrm{y})+f^{\prime}(\mathrm{x}) f(\mathrm{y}) \text { for all } \mathrm{x}, \mathrm{y} \in \mathbb{R} .
\]
Then, then value of \( \log _{\mathrm{e}}(f(4)) \) is
\( \mathrm{P} \)
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