Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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

share|cite|improve this question
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 $.

share|cite|improve this answer
    
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 $y$.

share|cite|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.