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.