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Differential Equations question

2025 · 22 Jan · Shift 1 · Q36

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JEE Main
Mathematics
Differential Equations
2025 · 22 Jan · Shift 1 · Q36

Differential Equations question

2025 · 22 Jan · Shift 1 · Q36

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let

f(x)

be a real differentiable function such that

f(0)=1

and

f(x+y)=f(x) f^{\prime}(y)+f^{\prime}(x) f(y)

for all

x, y \in \mathbf{R}

. Then

\sum_{n=1}^{100} \log _e f(n)

is equal to :

A
2406
B
5220
C
2525
D
2384

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