If y is a function of x and
x2 + y2 = 16,
We take derivatives of both sides, using the prime notation to mean "derivative with respect to x".
(x2 + y2)' = (16)'
Since the derivative of a constant is 0,
(x2 + y2)' = 0
Now we go to work on the left-hand side. While we don't have a formula for y, we know that y is a function of x. Thereforeany derivatives involving y need to use the chain rule.
Now we solve for y'.