Exercise 13, § 2

One terms the symmetric derivative of a vector function $f$ at a point $x_0$ interior to the interval where $f$ is defined, the limit (when it exists) of $\frac{f(x_0 + h) - f(x_0 - h)}{2h}$ as $h$ tends to 0 remaining > 0.

a) Generalize to the symmetric derivative the rules of calculus established in § 1 for the derivative.

b) Show that theorems 1 and 2 of § 2 remain valid when one replaces the words "right derivative" by "symmetric derivative".