How Does Taylor's Series Apply to Multivariable Functions?

[Mattofix]

Homework Statement

http://img99.imageshack.us/img99/9044/tayloriq0.th.jpg

Homework Equations

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The Attempt at a Solution

I have no idea - please help...

 

[HallsofIvy]

Are you serious? You have never seen Taylor's series before and your teacher assigned a problem like this? klWhat an evil person!

The Taylor's series, at (0,0), for a function, f(x,y), of two variables is given by
$$f(0,0)+ f_x(0,0)x+ f_y(0,0)y+ \frac{f_{xx}(0,0)}{2}x^2+ \frac{f_{xy}(0,0)}{2}xy+ \frac{f_{yy}(0,0)}{2}y^2+ \frac{f_{xxx}(0,0)}{6}x^3+ \frac{f_{xxy}(0,0)}{6}x^2y+ \frac{f_{xyy}(0,0)}{6}xy^2+ \frac{f_{yyy}(0,0)}{6}y^3+ \cdot\cdot\cdot$$

Can you find those derivatives?