3.7 Implicit Differentiation Objective: SWBAT find derivatives using implicit differentiation

Up until now we have been dealing with explicit functions (functions that are already solved for y). Implicit functions are functions that have not been solved for y. There are some functions for which it is not possible to solve for y, or you may not be sure how to do it. However, we can still find the derivative for a function that is written implicitly. – In order to do so, we have to treat the function y as if it could be written as a function of x. – y is going to be the inside function and we will use a chain rule effect to differentiate.

As previously mentioned, a problem with the alternative approach is that it sometimes may be very difficult or even impossible to solve for y. Therefore, implicit differentiation is usually the approach to utilize.