Section 3.2   The derivative as a function

Differentiate- find the derivative

Some different ways derivatives will be expressed are:

A function is differentiable (if you can take the derivative) at a if exists on open interval , , ,  if it is differentiable at every number in the interval

A function is not differentiable if there is a sharp turn in the graph (a point somewhere), a vertical tangent, and/or it is discontinuous

Examples:

Find the derivative of the given function using the definition of derivatives. State the domain of the function and its derivative.

Example 1:

 then plug in the function to get

domain of f = the domain of all reals

Example 2:

 then plug in the function to get

  =

 =   =  =

      the domain of   the domain of

Example 3:

=

the domain of