(4) Let f: R² R2 be defined by
f(x, y) = (2x + 3y + y², 3x - 2y = xy)
Use directly the definition of the derivative to show that f is differentiable at the origin and compute f'(0,0).
Hint: If the derivative exists, it is in L(R², R²), so it can be represented by a 2x2 matrix.