<s>[INST] The derivative of $ \ln\left(\frac{x+2}{x^3-1}\right)$ I know it is a simple question, but what would be the next few steps in this equation to find the derivative?
$$f(x)= \ln\left(\frac{x+2}{x^3-1}\right)$$
 [/INST] I would NOT use the chain rule before doing this:
\begin{align}
f(x) = \ln\frac{x+2}{x^3-1} & = \ln (x+2) - \ln(x^3-1) \\[10pt]
& = \ln(x+2) - \ln((x-1)(x^2+x+1)) \\[10pt]
& = \ln(x+2) - \ln(x+1) - \ln(x^2+x+1).
\end{align}
</s>