Calculation of Derivatives

Abstract

The statement g(x) = 1 has been discussed in two cases. In the first, the definition of the derivative, g is the quotient

$$ g\left( x \right) = \frac{{f\left( x \right) - f\left( a \right)}}{{x - a}} $$

where f is a function defined on some interval and a is an interior point of the interval (i.e., not an end point). In this case g is defined at every point suffi¬ciently close to a, except for a itself.