Archive for the ‘Implicit Differentiation’ Category

In the spirit of consistency, several additional examples supplementing my introduction to related rates are included here. As seen in the first example below, past concepts are revisited and, in turn, connected to newly introduced ones. Mixing things up from that point on provides students with a variety of perspectives on the same theme that serves to further cement understanding.


Separable Differential Equation

Circle area Derivative


Three Approaches to Related Rates

Circle area Differential Equation


Application to Conical Container

DiffEqua Realted Rates2



Rate of Change of Arc Length



The approach to solving each of these related rate problems is the same; identify what is known, what is desired and then connect the two.


Thanks for reading.

Having previously determined the derivative of ln(x), we now have that at our disposal to show one perspective of the product and quotient rules of differential calculus. A quick excursion to “implicit differentiation land” and a review of the chain rule will set things up nicely to meet our objectives here.

Implicit Diff and Chain Rule


Product and Quotient Rules

Product Quotient Rules

Modified Product Rule

Modified Product Rule

Thanks for reading.