Answer
See explanation
Work Step by Step
Work Step by Step
Step 1 In this problem, we will compare the process of implicit differentiation with the use of the following formula: \[ \frac{dy}{dx} = -\frac{\partial f / \partial x}{\partial f / \partial y} \] This formula is based on the relationship between partial derivatives and can be applied when we have the equation of the form $f(x, y) = c$. Essentially, we are performing implicit differentiation using this formula. Step 2 Let's delve into the background of the formula: \[ \frac{dy}{dx} = -\frac{\partial f / \partial x}{\partial f / \partial y} \] We can use this formula when dealing with special cases where $ f(x, y) = c$. In such cases, implicit differentiation becomes more manageable by employing this formula. Step 3 In a more general case of implicit differentiation, we differentiate every term with respect to the independent variable (typically $x$). Afterward, we use the chain rule to simplify further. Once we've simplified each term, we proceed to solve for the desired derivative by rearranging the terms and isolating the derivative.