Finding y' using implicit differentiation at given point

In this math example, we are given an equation and tasked with using implicit differentiation to find dy/dx = y'. To do so, we walk through the steps of using the power rule and product rule, one term at at time. We are careful to include y' = dy/dx when we take the derivative of a term that has the variable y. y' is then isolated on one side by itself and we use the given point to substitute in for each x and y on the other side of the derivative. Our solution is then simplified completely.