Math Is Fun Forum

In the first example of implicit differentiation topic (https://www.mathsisfun.com/calculus/implicit-differentiation.html) you are differentiating x² + y² = r² with respect to x. According to partial derivative article
(https://www.mathsisfun.com/calculus/derivatives-partial.html), to find derivative with respect to x we should treat all other variables as constant then why only r² is treated as constant in the example? Why not y²? Also why we cannot find derivative of y² using power rule? Why you use chain rule only for y²? Last few topics of calculus are hard to understand. Please help me...