Solution needed

Calculus Level 4

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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