Conventional variables to use for Chain Rule

[ressie]

What are the conventional variables to use for Chain Rule?
My textbook (Cambridge) use 'u' first then use 'w' if needed. They use 'v' when using the Product or the Quotient Rule.
What if I need another variable? I want to go beyond u and w, but I can't find any list of conventional variables to use. I'm aware that I can use any variables such as a, b, c but I don't like diverging from the convention. (I attached a sample step by step solution from my textbook)

[fun_jirachi]

It doesn't matter as long as your mathematical logic is sound. As an example, you could differentiate with respect to ampersand if you really wanted to (given your working out was logical). If you really dislike 'unconventional' variables, common ones include \(u\) and \(t\) (\(t\) is most often used for parameterization, \(u\) for change of variables). Additional ones include \(v, w, z\). \(k\) and \(n\) are usually used for indices and/or summation, amongst other uses. I haven't done VCE but I don't expect you to have to worry about using the chain rule more than twice, so just use whatever suits you

Hope this helps

[Sine]

What are the conventional variables to use for Chain Rule?
My textbook (Cambridge) use 'u' first then use 'w' if needed. They use 'v' when using the Product or the Quotient Rule.
What if I need another variable? I want to go beyond u and w, but I can't find any list of conventional variables to use. I'm aware that I can use any variables such as a, b, c but I don't like diverging from the convention. (I attached a sample step by step solution from my textbook)

As above, it really doesn't matter as long as the maths is valid. However, at least for methods for VCE the conventional variables are u for the chain rule and u and v for the product/quotient rule.

[S_R_K]

I'm going to disagree with the premise of your question - that you should introduce additional variables at all. Just write down the answer, eg:

\(\begin{aligned}[t] \frac{d}{dx}\left(\left(x + \sqrt{x^2+1}\right)^2\right) &= 2\left(x + \sqrt{x^2+1}\right) \times \left(1 + \frac{1}{2\sqrt{x^2+1}} \times 2x\right) \\
&= 2\left(x + \sqrt{x^2+1}\right) \times \left(\frac{\sqrt{x^2+1} + x}{\sqrt{x^2+1}}\right) \\
&= \frac{2\left(x + \sqrt{x^2+1}\right)^2}{\sqrt{x^2+1}}
\end{aligned}
\)

I've never seen a Methods exam question (or even a Specialist) exam question where writing down \(u= ...\) was worth doing.