Is there a function that...

[the1024b]

Is there a function that represents a curved line like a circle but that is only represented on the (+,+) zone of the graph?

[Nexus[Free-DC]]

Sure. Try this:

let x^* = (\sqrt{x})^2. This is equal to x for x>0 and undefined for x<0.

Now, your quarter circle is given by:

f(x) = \sqrt{1-(x^*)^2}

[the1024b]

and whats the derivative of that function?

Maybe i should put this on calculus?

[Chen]

The derivative is the same as that of a regular circle, except that you use (\sqrt{x})^2 instead of just x:

f'(x) = -\frac{(\sqrt{x})^2}{\sqrt{1-(\sqrt{x})^4}}

[uart]

There's no problem in putting restriction on the domain of the function as part of it's definition. Just use,

f(x) = +\sqrt{r^2 - x^2} : 0 \le x \le r

[matt grime]

You could just declare that the function "defining" the circle is undefined for negative x and takes the positive square root to avoid all this competely unnecessary behaviour.

[Integral]

Perhaps I am missing something, what is wrong with
f(x) = +\sqrt{r^2 - (x-h)^2} +k : h-r \le x \le h+r :k ,h\ge r