## 6.5. Differentiable Functions

### Examples 6.5.2(a):

- If
*f(x) = x*, then*= (x - c) / (x - c) = 1*so that*f'(x) = 1*for all*x*. - If
*f(x) = 1 / x*, then*= (1/x - 1/c) / (x - c) = (c - x) / (x - c) * 1 / (x c) = - 1 / c*, so that^{2}*f'(x) = - 1 / x*for all^{2}*x*not equal to zero.