Calculus Implicit Differentiation Application: Surface Area of Closed Box

In this calculus mathematical modeling example, we are create a function to represent the surface area of a closed box with a square base in terms of two variables. A picture of the given situation is drawn and we represent each of the sides of the box as we are creating the surface area formula. Then we substitute the given surface area into the formula. The derivative is found as the product rule is used as we do implicit differentiation to our equation. At this point, dy/dx=y' is part of our equation and we work the steps to isolate it on one side by itself. After this is complete, the given values of x and y are substituted into the formula and our solution is simplified completely. This calculus application of derivatives using implicit differentiation is very useful when we have a multivariable function.