<s>[INST] differentiate $(2x^3 + 3x)(x − 2)(x + 4)$ So, I'm really stuck on this problem.
Differentiate $(2x^3 + 3x)(x − 2)(x + 4)$
This is what I come up with $10x^4+16x^3+39x^2+6x-18$.
But, the answer in the book has $16x^4$ as the leading term
Here's my work:
$(2x^3+3x)d/dx(x^2+2x-8)+(x^2+2x-8)d/dx(2x^3+3x)$
$(2x^3+3x)(2x+2)+(x^2+2x-8)(6x^2+3)$
$(4x^4+4x^3+6x^2+6x+6x^4+12x^3-48x^2+3x^2+6x-24)$
$=10x^4+16x^3+39x^2+6x-18$
 [/INST] I would do it simply by expanding and then repeatedly using the Power Rule (using the Product Rule would be overkill I think):
$$
(2x^3+3x)(x-2)(x+4) = 2x^5+4x^4-13x^3+6x^2-24x.
$$
Now differentiate with respect to $x$, obtaining
$$
\frac{d}{dx}(2x^5+4x^4-13x^3+6x^2-24x) = 10x^4+16x^3-39x^2+12x-24.
$$
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