implicit differentiation with square roots

In this math example, we are given an equation that contains two variables, both under square roots. We find the derivative, y' = dy/dx, and evaluate it at a given point by using implicit differentiation. Each step of this process is gone through and explained as we use the power rule to take our derivatives, then rearrange the equation to isolate y' on one side by itself. Because of the square roots, we rewrite them as fractional exponents and use the power rule, that makes us end up with negative exponents. These are rewritten as positive when simplifying. sqrt(x)+sqrt(y)=