Let be differentiable function satisfying for all

MATHEMATICS · Single correct · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let ff be differentiable function satisfying f(xy)=f(x)−f(y)f\left(\frac{x}{y}\right) = f(x) - f(y) for all x,y>0x, y > 0. If f′(1)=1f'(1) = 1, then f(x)f(x) is (1) 2log⁡ex2 \log_e x (2) 3log⁡ex3 \log_e x (3) log⁡ex\log_e x (4) 12log⁡ex\frac{1}{2} \log_e x

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