Posts Tagged ‘Derivative’

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

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Four towns (A, B, C, D) are situated to form a square with side length of 1 unit. Determine the minimum length of roadway that will link these four towns together.

View the James Grime video first.

Minimum Length

Click on the following link for an interactive exploration: GeoGebra


The graph below shows the length of roadways linking these towns as a function.

Length as a Function of  “x”

Four Towns Minimum

Click on the link provided here to determine local minimum.


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