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Question Number 204426 by universe last updated on 17/Feb/24
$$\:\:\mathrm{let}\:\mathrm{a}\:,\:\mathrm{b}\:>\mathrm{0}\:\:\mathrm{find}\:\mathrm{all}\:\mathrm{differentiable}\:\mathrm{function} \\ $$$$\:\:\:\mathrm{f}:\left(\mathrm{0},\infty\right)\rightarrow\left(\mathrm{0},\infty\right)\:\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\:\:\:\:\mathrm{f}'\left(\frac{{a}}{\mathrm{x}}\right)\:\:=\:\:\frac{\mathrm{bx}}{\mathrm{f}\left(\mathrm{x}\right)}\:\:\:\:,\:\:\:\forall\:\mathrm{x}>\mathrm{0} \\ $$