Taylor expansion for two-variable function.

Question

Expand the function $ f (x, y) = e ^ {x-2y} $ in a Taylor series at the point $ (- 1,2) $. Please help me with it. I don't know how to do it although I did try to do it.

Answer 1

$f(-1,2)=e^{-5}$

$f_x(-1,2))=e^{-5}$

$f_y(-1,2))=-2e^{-5}$

$f_{xx}(-1,2)=e^{-5}$

$f_{yy}(-1,2)=4e^{-5}$

$f_{xy}(-1,2)=-2e^{-5}$...

Then we have:

$f(x,y)=e^{-5}+ e^{-5}(x+1)-2e^{-5}(y-2)+1/2!(e^{-5}(x+1)^2-2*2e^{-5}(x+1)(y-2)+4e^{-5}(y-2)^2)+...$