Differentiable Function Sum (Jee Mains)

Continuity and Differentiability

Hard

Differentiable Function Sum

Let ƒ(x) be a real differentiable function such that ƒ(0) = 1 and ƒ(x + y) = ƒ(x)ƒ'(y) + ƒ'(x) ƒ(y) for all x, y ∈ R. Then $\sum\limits_{n = 1}^{100} {{{\log }_e}ƒ(n)}$ is equal to :

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