 I want to make sure that you understand the partial derivatives of the u and v velocity with respect to x and y, because we will soon be using these terms a lot. Let's start with the partial derivative u with respect to x. Consider a constantly increasing x, so that change in x is positive. As x increases, u becomes initially less negative, hence the positive change, then becomes positive, another positive change, and then becomes more positive, another positive change. Since the change in u and the change in x are both always positive, the partial derivative is positive, greater than zero. Look at the case where partial derivative is less than zero or negative. As x increases, u becomes less positive, hence a negative change, then becomes negative, another negative change, and then becomes more negative, another negative change. Since the change in u is always negative with a positive change in x, the partial derivative is always negative. The same logic applies to the partial derivative of v with respect to y. Up is positive for y, so you should look at how v changes as y becomes more positive. Look at the case of the change in u with respect to y. It does not matter that u is in the x direction perpendicular to y, because we are interested in how u changes as a function of y. Let's look at what happens as y becomes more positive. On the left, u becomes less negative, a positive change in u, then positive, then more positive. Thus the partial derivative is a positive change in u over a positive change in y, and therefore is positive for greater than zero. The change in u with respect to y is always positive in this case. Using the same logic on the right, we see that the change in u with respect to y is always negative, and because the change in y is positive, the partial derivative is negative or less than zero. The same logic applies to the partial derivative of v with respect to x. To the right is positive for x, so you can determine how v changes as x becomes more positive to see whether the partial derivative is positive or negative.