The power of a Dual number should read:

where it is noted that (n-1) is the exponent and not a multiplier. This is due to a mising ^ in the LaTeX file.
Additionally, when f(x+e_x, y+e_y) is expanded it should result in:

noting the omission of the y term in the first term.
The power of a Dual number should read:

where it is noted that (n-1) is the exponent and not a multiplier. This is due to a mising
^in the LaTeX file.Additionally, when
f(x+e_x, y+e_y)is expanded it should result in:noting the omission of the
yterm in the first term.