JEE Advanced_2018_S2 ( Mathematics 2018 Q-11 ) - Competishun – Live JEE & NEET Courses and Exam Prep

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JEE Advanced 2018

Paper-2 2018

Question

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

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