Consider the following problem from Chapter 3 of *Curves and Surfaces*, 2nd edition, by Montiel and Ros:

Now, for me it is easy to see that $$ (dF_r)_p(v) = v + r (dN)_p(v), \quad v \in T_pS. $$ If $v = e_i$ is a principal direction, $$ (dF_r)_p(e_i) = (1 + rk_i)e_i. $$

This differs from what the books asks us to show. What am I missing? Is it really a typo?