The potential energy of a force field $\hat F$ is given by $v(x,y)=\cos (x+y)$ . The force acting on the particle at position given by coordinate $(0, \large\frac{\pi}{4})$ is

Question

\[(a)\;\frac{-1}{\sqrt 2}(\hat i+\hat j) \quad (b)\;\frac{1}{\sqrt 2}(\hat i+\hat j) \quad (c)\;\bigg(\frac{1}{2}\hat i+\frac{\sqrt 3}{2}\hat j\bigg) \quad (d)\;\bigg(\frac{1}{2}\hat i-\frac{\sqrt 3}{2}\hat j\bigg)\]