# Taylor expansion with two variables

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.

• Also the symbol $y$ is used, it's not a variable. Notice the function is defined from $\mathbb R$ to $\mathbb R$. The $y$ is just a constant multiplying $e^{x^2}$. – Matthew Leingang Feb 26 at 20:07
• PS Actual Taylor expansion with two variables is a much more involved process. A function $f(x,y)$ has two first derivatives and four second derivatives (although two of them are usually the same). – Matthew Leingang Feb 26 at 20:08
• Please use MathJax to format your posts. You will get a much more positive response if you questions are easy to read. – saulspatz Feb 26 at 20:13
• Oh yes you are right about y. I'm sorry. – Aurangzeb Rathore Feb 26 at 20:25