What does implicit function mean by deriving x The simplest x ^ 2 = 1-y ^ 2 knows how to find the derivative on the left, but I don't understand it on the right. Why is y.y '? Isn't y derivative 1? I don't understand the definition well!

What does implicit function mean by deriving x The simplest x ^ 2 = 1-y ^ 2 knows how to find the derivative on the left, but I don't understand it on the right. Why is y.y '? Isn't y derivative 1? I don't understand the definition well!

Because y is actually an explicit function of X, but we can't write out how much y = x, we use an expression that doesn't put the dependent variable on one side alone. Y is a function, and both sides of the equation are deriving from X. according to the chain rule, y square first differentiates the outer function by 2Y, and then differentiates the inner function by Y ', of course y'
The important thing is that both sides are derivations of X, not both sides of X and y