implicit differentiation problem includes sine function

In this calculus math example, we are presented with a complicated equation and tasked with finding the derivative dy/dx = y'. We walk through the steps by planning out which derivative rules we will be utilizing first. This calculus problem requires us to use the product rule, chain rule, power rule, and know the derivative of the trigonometric function: sine. Each step is explained as we work through them. dy/dx is highlighted because it is the part of the problem that needs to be solved for in the end. To do so, after taking the derivative, we move all terms that contain dy/dx to one side of the equation and all terms that do not contain a dy/dx to the other side of the equation. dy/dx is then factored out of each term and both sides are divided by the other factor from that side of the equation. This results in dy/dx being on one side by itself and we have our derivative.