Two results for the same (?) derivative $f(x) = \frac{y}{x}$

Question

I was looking for a method to differentiate $f(x) = \frac{y}{x}$. Entering "differentiate $f(x) = y/x$" into WolframAlpha gives result:

$$ f'(x) = \frac{-y}{x^2} $$

The main step of computing this derivative is:

$$ f'(x) = y\frac{d}{dx}\big(\frac{1}{x}\big) $$

So it factors out constant $y$ and uses power rule to obtain $\frac{-1}{x^2}$. When I instead enter "differentiate y/x", I get result:

$$ \frac{d}{dx}\big(\frac{y}{x}\big) = \frac{xy'(x) - y}{x^2} $$

It is computed using the quotient rule:

$$ \frac{d}{dx}\big(\frac{u}{v}\big)=\frac{v \frac{du}{dx}-u \frac{dv}{dx}}{v^2} $$

How to explain the two different results?

Answer 1

It's simply because you consider $y$ as a constant and Wolfram considers that $y$ is a function $y(x)$ of $x$.