How should i approximate this? Find the taylor series for the given function about the given point.
$$f(x,y)= e^{x^2+y^2}$$
My solution I thought was $e^{x^2}\cdot e^{y^2}$.
How should I make a summation about this?. 

$e^{x^2} = 1 + x^2 + \frac 12 x^4 + \frac 16 x^6\cdots\\
(e^{x^2})(e^{y^2} = (1 + x^2 + \frac 12 x^4 + \frac 16 x^6\cdots)(1 + y^2 + \frac 12 y^4 + \frac 16 y^6\cdots)\\
(e^{x^2})(e^{y^2} = 1 + x^2 + y^2 + \frac 12 (x^4 + y^4 + 2x^2y^2)+\frac 16 (x^6 + y^6 + 3x^4y^2 + 3x^2y^4) \cdots$
I am just multiplying the terms from one expansion by the terms in the other expansion.
but more generally
$f(x,y) = f(x_0,y_0) + f_x (x_0,y_0)(x-x_0) + f_y (x_0,y_0)(x-x_0) + \frac 12 (f_{xx}(x_0,y_0)(x=x_0)^2 + 2f_{xy}(x_0,y_0)(x-x_0)(y-y_0)+f_{yy}(x_0,y_0)(y-y_0)^2)$ 
