Dini Derivatives Properties proof.

Question

Theorem. Let $f$ be defined and finite on the interval $[a,b]$. Then $$\overline{D}f(a) = D^{+} f(a)$$ $$\underline{D} f(a) = D_{+} f(a)$$ $$\overline{D} f(b) = D^- f(b)$$ $$ \underline{D} f(b) = D^- f(b)$$ if $x_0 \in (a,b)$ $$\overline{D} f(x_0) = \sup \{ D^+ f(x_0), D^- f(x_0) \}$$ $$ D^+ (-f(x)) = - D_+ f(x)$$ Can someone help me with proof these two properties. I don't know where to start and it's my first meeting with Dini dervatives. $\overline{D}$-upper derivative, $D^-$ left upper derivative.