Let $\mathbf{F} ( x, y ) = \frac{-y \mathbf{i} + x \mathbf{j}}{x^{2} + y^{2}}$ and let $C$ be the circle $\mathbf{r} \left( t \right) = \left( \cos t \right) \mathbf{i} + \left( \sin t \right) \mathbf{j}$, $0 \leq t \leq 2\pi$.

A. Compute $\frac{\partial Q}{\partial x}$

Note: Your answer should be an expression of $x$ and $y$; e.g. "3xy - y"

B. Compute $\frac{\partial P}{\partial y}$

Note: Your answer should be an expression of $x$ and $y$; e.g. "3xy - y"

C. Compute $\int_C \mathbf{F} \cdot d\mathbf{r}$

Note: Your answer should be a number

D. Is F conservative in the whole $xy$-plane? ? Yes No