Exercise 7, § 1

Let $f$ be a real function defined on an interval $I \subset \mathbf{R}$, admitting a right derivative $f'_d(x_0) = 0$ at a point of I, and let g be a vector function defined on a neighbourhood of $y_0 = f(x_0)$, having a right derivative and a left derivative (not necessarily equal) at this point. Show that $g \circ f$ has a right derivative equal to 0 at the point $x_0$.