Suppose $\displaystyle y^{\,\prime} = f(x,y) = \frac{xy}{\cos\!\left(x\right)}$.

1. $\displaystyle \frac{\partial f}{\partial y} =$ help (formulas)
   
   
2. Since the function $f(x,y)$ is Choose continuous not continuous at the point $(0,0)$, the partial derivative $\frac{\partial f}{\partial y}$ Choose exists does not exist and is Choose continuous not continuous at and near the point $(0,0)$, the solution to $y' = f(x,y)$ Choose exists and is unique does not exist near $y(0) = 0$