(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the derivative of the function

[tex]g(x)=(1+4x)^5(3+x-x^2)^8[/tex]

2. Relevant equations

- Chain rule

- Power rule

3. The attempt at a solution

[tex]g(x)=(1+4x)^5(3+x-x^2)^8[/tex]

[tex]g(x)=(1+4x)^5\frac{d}{dx}(3+x-x^2)^8+(3+x-x^2)^8\frac{d}{dx}(1+4x)^5[/tex]

[tex]g(x)=(1+4x)^58(2x-1)(3+x-x^2)^7+(3+x-x^2)^820(1+4x)^4[/tex]

...

This is where I'm stuck. Both my calculator and the book tell me that the solution is

[tex]4(4x+1)^4(x^2-x-3)^7(21x^2-9x-17)[/tex]

All I want to know is how they get to this result from the step I got stuck at above. I don't see how they arrive at that last polynomial :/

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# Derivative of [(1+4x)^5][(3+x-x^2)^8]

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