Q.Let f(x) be a real differentiable function such that f(0) = 1 and f(x + y) = f(x)f'(y) + f'(x)f(y) for all x, y $\in \mathbb{R}.$ Then $\sum_{n=1}^{100} \log_{e} f(n)$ is equal to:

2384

2525

5220

2406

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Q.Let f(x) be a real differentiable function such that f(0) = 1 and f(x + y) = f(x)f'(y) + f'(x)f(y) for all x, y ∈R.\in \mathbb{R}.∈R. Then ∑n=1100log⁡ef(n)\sum_{n=1}^{100} \log_{e} f(n)∑n=1100​loge​f(n) is equal to: