<s>[INST] Derivative of $ y = (2x - 3)^4 \cdot (x^2 + x + 1)^5$ $$ y = (2x - 3)^4 \cdot (x^2 + x + 1)^5$$
I know that it should be the chain rule and product rule used together to get the answer
$$ y = \frac{dx}{dy}((2x - 3)^4) \cdot (x^2 + x + 1)^5 +  \frac{dx}{dy}(x^2 + x + 1)^5 \cdot (2x - 3)^4 $$
this gives me something ridiculous like this
$$8(2x-3)^3 \cdot (x^2 + x + 1)^5 + (x^2 + x + 1)^4 \cdot (2x+1) (2x-3)^4$$
This is wrong and I keep getting it, I don't know how to simplify it without expanding everything.
The book Houdini's out $(2x -3)^3 (x^2 + x + 1)^4 (28x^2 - 12x - 7)$
 [/INST] We have $$8(2x-3)^3 * (x^2 + x + 1)^5 + 5(x^2 + x + 1)^4 (2x+1) (2x-3)^4\\=
(2x-3)^3(x^2+x+1)^4(8(x^2+x+1)+5(2x+1)(2x-3))
\\=(2x-3)^3(x^2+x+1)^4(8x^2+8x+8+20x^2-20x-15)\\=
(2x-3)^3(x^2+x+1)^4(28x^2-12x-7)$$  
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