3. The function $f^h$ in the triangular element shown below is a piecewise function which is expressed as a sum of three linear shape functions
$f^h(x, y) = \sum_{i=1}^3 a_i \phi_i$
Shape functions:
$\phi_1(x, y) = \frac{y(-x_2 + x_3)}{2A} + \frac{x(y_2 - y_3)}{2A} + \frac{-x_3y_2 + x_2y_3}{2A}$
$\phi_2(x, y) = \frac{y(x_1 - x_3)}{2A} + \frac{x(-y_1 + y_3)}{2A} + \frac{x_3y_1 - x_1y_3}{2A}$
$\phi_3(x, y) = \frac{y(-x_1 + x_2)}{2A} + \frac{x(y_1 - y_2)}{2A} + \frac{-x_2y_1 + x_1y_2}{2A}$
Where A is the area of the element:
$A = \frac{1}{2}(x_3(y_1 - y_2) + x_1(y_2 - y_3) + x_2(-y_1 + y_3))$
If $[a_1 \quad a_2 \quad a_3] = [0.5 \quad 1 \quad 2]$, compute $\nabla f^h$ at point $P = (x_p, y_p)$. (6 points)