Archive for the ‘Implicit Differentiation’ Category

In the spirit of consistency, several additional examples supplementing my introduction to related ratesย 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

DiffEquaRelatedRatesArcLength

 

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 ofย 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.