JEE Math Practice Question
Let $$f: \mathbb{R}-\{0\} \rightarrow \mathbb{R}$$ be a function satisfying $$f\left(\frac{x}{y}\right)=\frac{f(x)}{f(y)}$$ for all $$x, y, f(y) \neq 0$$. If $$f^{\prime}(1)=2024$$, then
- A.$$x f^{\prime}(x)+2024 f(x)=0$$
- B.$$x f^{\prime}(x)-2023 f(x)=0$$
- C.$$x f^{\prime}(x)-2024 f(x)=0$$
- D.$$x f^{\prime}(x)+f(x)=2024$$
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