Picture below is from the section 2 of Chapter 5 of do Carmo's Riemannian Geometry. I can't calculate the red lines.
What I try: $$ \frac{\partial f}{\partial s}(t,0) = (d\exp_p)_{\frac{t}{a}v(0)} \frac{t}{a}v'(0) = (d\exp_p)_{tv} \frac{t}{a}\omega $$ why in the first red line, there is not $\frac{1}{a}$ ?
Besides, I find the Lee's book. There is not a similar proposition. In fact, I feel this proposition has flow.
