<s>[INST] Simplify this, how to? The original function is $$f(x)=\cfrac{3x^3}{\cfrac{1}{x}} $$
It's the quotient rule I'm using so: 
$$ f^\prime\left(x\right) =\dfrac{9x^2\cdot\cfrac{1}{x} -  3x^3 \cdot \left(-x^{-2}\right)}{\dfrac{1}{x^2}}$$ 
I suck at simplifying, so I just need to get the hang of it. I've done some already, but this one is troubling me. Thanks. Oh, and STEP BY STEP please. 
 [/INST] $$\dfrac{9x^2 \cdot \frac 1x - 3x^3 \cdot -x^{-2}}{1/x^2} = \dfrac{9x^2 \cdot \frac 1x - 3x^3 \cdot \frac{-1}{x^2}}{1/x^2} = \dfrac{9x +3x}{1/x^2} = x^2(12x) = 12x^3$$
Note, however that $$f(x) = \dfrac {3x^3}{\frac 1x} = x(3x^3) = 3x^4 \implies f'(x) = 12x^3$$
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