Consider the map $F: \mathbb{RP}^2 \to \mathbb{RP}^3$ given by $$[x:y:z] \to [x^2+y^2:xy:x^2+z^2:xz]$$
Find the points in $\mathbb{RP}^2$ where $F$ doesn't have rank $2$
I am confused about how to find the differential of the map. Any hint would suffice.
Thanks for the help!!