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If f (x/y)= f(x)/f(y) ,AA y, f (y)!=0 an...

If `f (x/y)= f(x)/f(y)` ,`AA y, f (y)!=0` and `f' (1) = 2`, find f(x) .

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To solve the problem given the functional equation \( f\left(\frac{x}{y}\right) = \frac{f(x)}{f(y)} \) for all \( y \) such that \( f(y) \neq 0 \) and the condition \( f'(1) = 2 \), we will follow these steps: ### Step 1: Differentiate the functional equation We start with the functional equation: \[ f\left(\frac{x}{y}\right) = \frac{f(x)}{f(y)} \] Differentiating both sides with respect to \( x \): ...
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