# Solution needed

Calculus Level 3

Let $$f$$ be a differentiable function satisfying the condition $$f\left(\frac{x}{y}\right) = \dfrac{f(x)}{f(y)}$$ for all $$x,y$$.

If $$f'(1)=2$$,

Find $$f'(x)$$.

Details and Assumptions:-

• $$f'(x)=\dfrac{d(f(x))}{dx}$$ and $$f'(k)$$ is the value of $$\frac{d(f(x))}{dx}$$ at $$x=k$$.
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