<s>[INST] Differentiation of $f(x)=2x(2+3x^2)^3$ The question:

Differentiate $f(x)=2x(2+3x^2)^3$.

How do I approach this problem? Do I only have to use the product rule...? I have the answer but I don't know how to get there.
Here is my attempt to this problem: 
$$\frac{df}{dx}=(2)(2+3x^2)^3 + (2x)(6x)(3)(2+3x^2)^2 = \\ =(2+3x^2)^2 [(2)(2+3x^2) + (2x)(6x)(3)] = \\ = (2+3x^2)^2 [(4+6x^2) + 36x^2] = \\ = (2+3x^2)^2 (42x^2+4)$$
 [/INST] You get the right answer:
$$(2+3x^2)^2 (42x^2+4)=(2+3x^2)^2 \cdot 2 \cdot (21x^2+2)$$
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