# why constant derivatives?

Really simple question here.

Say $f(x)$ and $g(y)$ then why if

$\frac{d f(x)}{dx} = \frac{d g(y)}{dy}$

then both derivatives are constant?

Thank you all very much

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Notice that $\dfrac{d g(y)}{dy}$ does not depend on $x$ because it is the partial derivative of a function $g$ with respect to $y$. $x$ is not allowed to vary in this expression. Thus, $\dfrac{d f(x)}{dx}$ does not depend on $x$, because the other expression does not depend on $x$.
As Damien L has said, the same is true for $y$.
Because $g$ is a constant function of $x$, so $\frac{df}{dx}$ is equal to a constant function of $x$.
Same for $f$ and $y$.