What are most ways to differentiate the same function?

Question

An example of a function that relates to my question: $f(x)=\frac{x^3\left(2x+1\right)^2}{x^2}$ with $x>0$.

That function could be differentiated (at least) 5 different ways using rules.

1. Simplify, expand and differentiate each term: $f(x)=4x^3+4x^2+x$ then $f'(x)=12x^2+8x+1$
2. Product rule: $f(x)=x(2x+1)(2x+1)$ then $f'(x)=(1)(2x+1)(2x+1)+(x)(2)(2x+1)+(x)(2x+1)(2)=12x^2+8x+1$
3. Chain rule with product rule : $f(x)=x\cdot(2x+1)^2$ then $f'(x)=(1)(2x+1)^2+(x)(2)(2x+1)(2)=12x^2+8x+1$
4. Logarithmic differentiation: $\ln\left(f(x)\right)=\ln\left(x\left(2x+1\right)^2\right)$ then $f'(x)=\left(\frac{1}{x}+2\cdot\frac{1}{2x+1}\cdot2\right)\left[x\left(2x+1\right)^2\right]=12x^2+8x+1$
5. Quotient rule with product rule: $f'(x)=\frac{\left(\left(3x^2\right)\left(2x+1\right)^2+\left(x^3\right)\left(2\left(2x+1\right)2\right)\right)x^2-\left(x^3\left(2x+1\right)^2\right)2x}{\left(x^2\right)^2}=12x^2+8x+1$
6. (And then, there is the limit definition of the derivative)

The purpose of the question is to introduce new ways of differentiating with functions that have been used previously. Also, students should think about which way is most efficient, but that only works if there are multiple (rule-based) ways of differentiating the same function.