Without finding the partial derivatives of $f\left(x,y\right)+e^x \cos (y)$, find the terms of up to and including order 4 in the Taylor series for f about (1,0).
I initially subbed in $y=0$ and tried to compute the Taylor series using the fact $$f(x,y)=f(1,0)+f_x(1,0)(y-0)+1/2! \cdot\ldots,$$ where I assumed all derivatives would equal $e$, but I now think is incorrect. How would I approach this question?