Topics:

• Definition of the derivative of a function at a point

• Differentiability

• Definition of the derivative function

Slideshow about definitions of derivatives:

MAT1475DefinitionOfDerivative-slideshow

Here are notes on two of the examples I worked in class: finding the derivative function of $f(x) = \frac{1}{x+1}$, and finding the derivative function of $f(x) = |x|$. Pay special attention in the second example to the way we need to use one-sided limits to see if the derivative exists at $x=0$. (It does not.)

MAT1475DerivativeDefinitionExamples

From now on I will post the homework in a separate post from the class notes. The homework assignment from today’s class is here.