i'm kinda stuck in a problem of the book Advanced Calculus of Watson Fulks. The problem is:
Calculate the directional derivative of $x^2+y^2-3xy$ on the point $P=(1,2)$ that goes to the tangent direction to the curve $y=x^3$.
Well, my problem is that i don't really get the idea of the tangent direction to a curve, i parametrize $y=x^3$ into $r(t) = (t, t^3)$ and then i derivate $r$ and that gives me $r'(t) = (1, 3t^2)$, but then i don't really know what to do.