Differentiation - quotient rule

To differentiate a quotient, use the quotient rule:

• bottom  x  derivative of top    -    top  x  derivative of bottom

                                          (bottom)²

The example below includes the use of the chain rule.
 

If you just wanted the gradient of the tangent at a particular point, there would be no reason to simplify and factorise.

Visual Calculus - discussion and simple problems.