## 6.5. Differentiable Functions

### Definition 6.5.1: Derivative

Let

*f*be a function with domain*in***D***, and***R***is an open set in***D***. Then the***R****derivative**of*f*at the point*c*is defined asIf that limit exits, the function is calledf'(c) =

**differentiable**at*c*. If*f*is differentiable at every point in*then***D***f*is called differentiable in*.***D**
Other notations for the derivative of *f* are
or
* f(x)*