## Related Rates (continued)

Posted: March 1, 2016 in Calculus: An Introduction, Differential Calculus, Differential Equations, Implicit Differentiation, Related Rates, The Derivative
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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

Three Approaches to Related Rates

Application to Conical Container

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.

## Product & Quotient Rules of Differentiation

Posted: February 18, 2016 in Differential Calculus, Implicit Differentiation, The Derivative
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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.

Product and Quotient Rules

Modified Product Rule