List of top Engineering Mathematics Questions on Derivatives

Let \( (x, y) \in \mathbb{R}^2 \). The rate of change of the real-valued function
\[ V(x, y) = x^2 + x + y^2 + 1 \] at the origin in the direction of the point \( (1, 2) \) is _____________ (round off to the nearest integer). 

Let \( (x, y) \in \mathbb{R}^2 \). The rate of change of the real-valued function \[ V(x, y) = x^2 + x + y^2 + 1 \] at the origin in the direction of the point \( (1, 2) \) is __________ (round off to the nearest integer).