Derivatives - optimization (minimum of a function) For which points of $x^2 + y^2 = 25$ the sum of the distances to $(2, 0)$ and $(-2, 0)$ is minimum?
Initially, I did $d = \sqrt{(x-2)^2 + y^2} + \sqrt{(x+2)^2 + y^2}$, and, by replacing $y^2 = 25 - x^2$, 
I got $d = \sqrt{-4x + 29} + \sqrt{4x + 29}$, which derivative does not return a valid answer.
Where did I commit a mistake?
Thank you!!

For better readability,    $$S=\sqrt{29+4x}+\sqrt{29-4x}$$
$$\dfrac{dS}{dx}=\dfrac2{\sqrt{29+4x}}\cdot4-\dfrac2{\sqrt{29-4x}}\cdot4$$
For the extreme values of $S,$ we need $\dfrac{dS}{dx}=0\implies29+4x=29-4x\iff x=0$
