I don't understand how to find the 
'difference quotient'. Could you please help me?
The problem is:

                       f(x) = x² + 1 

Learn the difference quotient formula:

                                f(x + h) - f(x)
difference quotient formula =  —————————————————
                                       h

First find f(x + h).  Start with:

      f(x) = x² + 1  

Replace both x's by (x + h) :

  f(x + h) = (x + h)² + 1

Simplify the right side.  To square a binomial
multiply it by itself:

  f(x + h) = (x + h)(x + h) + 1

Use FOIL:

  f(x + h) = x² + hx + hx + h² + 1 

Combine like terms:

  f(x + h) = x² + 2hx + h² + 1

Now substitute the following two into 
the numerator of the difference quotient formula:

  f(x + h) = (x² + 2hx + h² + 1)
      f(x) = (x² + 1)

                                f(x + h) - f(x)
difference quotient formula =  —————————————————
                                       h

Substituting into that numerator:

                         (x² + 2hx + h² + 1) - (x² + 1)  
difference quotient  =  ————————————————————————————————
                                       h

Remove parentheses in the numerator:

                          x² + 2hx + h² + 1 - x² - 1  
difference quotient  =  ————————————————————————————————
                                       h

The x² and the -x² cancel.  The +1 and the -1 cancel,
so we have:

                         2hx + h²   
difference quotient  =  —————————
                            h

Factor h out of the numerator:

                         h(2x + h)   
difference quotient  =  ———————————
                             h

Cancel the h's
                         1
                         h(2x + h)   
difference quotient  =  ———————————
                             h
                             1

difference quotient = 2x + h

Edwin