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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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2 Answers 2

up vote 2 down vote accepted

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 $.

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Thank you. I have now understood. –  Federico Mar 17 '13 at 19:40

Because $g$ is a constant function of $x$, so $\frac{df}{dx}$ is equal to a constant function of $x$.

Same for $f$ and $y$.

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