I'm required to do a Taylor series expansion of $f(ax, y+ \delta y)$ where $a$ is a constant and $\delta y$ is an increment of $y$. How would it be done?
This is probably a special case of the multi-variate Taylor series expansion of $f(x+ \delta x, y + \delta y)$, which i know how to do. i.e.
$ f(x + \delta x, y + \delta y)=f(x,y) + \frac{\partial f}{\partial x}\delta x + \frac{\partial f}{\partial y}\delta y + \frac{1}{2}\frac{\partial^2f}{\partial x^2}\delta x^2 + \frac{1}{2}\frac{\partial^2f}{\partial y^2}\delta y^2 + \frac{\partial^2f}{\partial x \partial y}\delta x \delta y$
Thank you.