Ok, so my original function is $\displaystyle f(x,y)=ln(x^2+y^2+1)$ and the problem states to take the partial derivative, first with respect to x, and then with respect to y, and find values of x and y such that both partial derivatives equal zero simultaneously. I understand that with a function such as $\displaystyle x^2+2x+1$ for instance, you can just do substitution with another function of the same type to cancel out one variable to find either x or y then plug it in to find the other variable...however, with this problem, my answers are as follows:

partial derivative with respect to x is $\displaystyle 2x / x^2+y^2+1$ and partial derivative with respect to y is $\displaystyle 2y / x^2+y^2+1$.

How would you guys recommend I solve this? Set the derivatives equal to each other and solve for a variable or something else?