I just finished studying about Taylor expansion from a beautiful video by 3Blue1Brown on youtube. I was trying it out on a few questions until I came across this and I don't understand how to handle Taylor Expansion with multiple variable. Could someone help provide and explanation and the solution?
Q) Compute the first three terms of Taylor Expansion of $f:\mathbb{R}\to\mathbb{R}$ given by
$$f(x) = ye^{x^2}$$
for $y\in\mathbb{R}$ around $x_0=0$. Please include intermediate steps.