Stationary points with 2 variables

Hi,

Locate and classify all of the stationary points of the function:

.

I have got as far as doing the partial derivatives for the terms but I am unsure if the partial derivatives I got are right

What I got for the derivatives so far are:

<-- unsure on this one

I am sure that after I have found these I am meant to equate them to zero (because they are stationary points) and then find x and y and then put the in one of the equations (I think its the original one if I remember correctly) and get the coordinates of the stationary points.