Often a relation (an expression in *x* and *y*), that has a graph but is not a function, needs to be analyzed. But the relation is not or cannot be solved for *y. *What to do? The answer is to use the technique of **implicit differentiation**. Assume there is a way to solve for *y* and differentiate using the Chain Rule. Whenever you get to the *y,*“differentiate” it by writing *dy/dx*. Then solve for *dy/dx*.

Here are several previous posts on this topic and how to go about using it.

Implicit Differentiation

Implicit Differentiation and Inverses

Implicit differentiation of parametric equations These are BC topics

A Vector’s Derivative These are BC topics

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Love ALL of your posts, articles, texts, insights, etc. Lin. They were very helpful to me as an AP Calculus teacher.

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Thank you.

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