$f \left (x, y \right) = \arctan \left (x y \right) + y \ln \left (x y \right)$ 일 때, 점 $\left (- 1, - 1 \right)$ 에서 기울기 벡터(gradient vector) $\nabla f \left (- 1, - 1 \right)$ 는?

• ①$\displaystyle \left (\frac{\sqrt {2}} {2}, - \left (\frac{\sqrt {2}} {2} \right) \right)$
• ②$\displaystyle \left (\frac{\sqrt {2}} {2}, \frac{3} {2} \right)$
• ③$\displaystyle \left (\frac{1} {2}, - \left (\frac{3} {2} \right) \right)$
• ④$\displaystyle \left (\frac{1} {2}, \frac{1} {2} \right)$