Linear approximation with two variables The problem I have is this:
Use suitable linear approximation to find the approximate values for given functions
at the points indicated:
$f(x, y) = xe^{y+x^2}$ at $(2.05, -3.92)$
I know how to do linear approximation with just one variable (take the derivative and such), but with two variables (and later on in the assignment, three variables) I'm a bit lost. Do I take partial derivatives and combine then somehow? Can someone guide me through a problem of this type? 
Thank you in advance.

Yes. Denoting the partial derivatives by $f'_x$ and $f'_y$, the formula is:
$$f(x_0+h,y_0+k)=f(x_0,y_0)+f'_x(x_0,y_0)h+f'_y(x_0,y_0)k+o\bigl(\lVert(h,k)\rVert\bigr).$$
