A two-dimensional temperature profile is given as $T=2 x^{2}+3 x y+y^{2}$. If $\hat{\boldsymbol{\imath}}$ and $\hat{\boldsymbol{\jmath}}$ are the unit vectors along $x$ and $y$ directions, respectively, which one of the following is the directional derivative of $T$ at the location $x=2, y=2$?
- $8 \hat{\imath}+12 \hat{\jmath}$
- $14 \hat{\imath}+10 \hat{\jmath}$
- $8 \hat{\imath}-12 \hat{\jmath}$
- $14 \hat{\imath}-10 \hat{\jmath}$
