HELP! trouble factoring while using the chain rule + the product rule

[macman2790]

I'm having trouble factoring using the chain rule with the product rule. the answer is in the book but i cant figure out how to factor it out correctly. Will someone please walk me through the factoring part, i'm having trouble with every problem like this and i have very many. the problem is:
differentiate:
y = (1+4x)^5 (3+x-x^2)^8

heres what I have so far:

y'= [5(1+4x)^4(4)](3+x-x^2)^8 + [8(3+x-x^2)^7*(1-2x)(1+4x^5)

now here's the answer:4(1+4x)^4(3+x-x^2)^7(17 + 9x - 21x^2)

Thanks in advance for the help.

 

[swiftaw]

y = (1+4x)^5 (3+x-x^2)^8

y' = 20(1+4x)^4 (3+x+x^2)^8 + 8(1-2x)(3+x-x^2)^7 (1+4x)^5

= 20(1+4x)^4 (3+x+x^2)^7 (3+x+x^2) + 8(1-2x)(3+x-x^2)^7 (1+4x)^4 (1+4x)

= 4(1+4x)^4 (3+x+x^2)^7 [5 (3+x+x^2) + 2 (1-2x) (1+4x)]

I think the answer follows from here by simplifying what is in [...]

 

[macman2790]

y = (1+4x)^5 (3+x-x^2)^8

y' = 20(1+4x)^4 (3+x+x^2)^8 + 8(1-2x)(3+x-x^2)^7 (1+4x)^5

= 20(1+4x)^4 (3+x+x^2)^7 (3+x+x^2) + 8(1-2x)(3+x-x^2)^7 (1+4x)^4 (1+4x)

= 4(1+4x)^4 (3+x+x^2)^7 [5 (3+x+x^2) + 2 (1-2x) (1+4x)]

I think the answer follows from here by simplifying what is in [...]

thank you very much, i should have a bit of an easier time simplifying the rest of the 15 product rule + chain rule problems😀

 

[macman2790]

= 20(1+4x)^4 (3+x+x^2)^7 (3+x+x^2) + 8(1-2x)(3+x-x^2)^7 (1+4x)^4 (1+4x)

= 4(1+4x)^4 (3+x+x^2)^7 [5 (3+x+x^2) + 2 (1-2x) (1+4x)]

does anyone mind telling me why 2(1+4x)^4 is simplifying to 4(1+4x), its just too late for me lol.😀

 

[swiftaw]

= 20(1+4x)^4 (3+x+x^2)^7 (3+x+x^2) + 8(1-2x)(3+x-x^2)^7 (1+4x)^4 (1+4x)

= 4(1+4x)^4 (3+x+x^2)^7 [5 (3+x+x^2) + 2 (1-2x) (1+4x)]

does anyone mind telling me why 2(1+4x)^4 is simplifying to 4(1+4x), its just too late for me lol.😀

?

Not sure where you are looking?

I split the 20 up into 4*5, the 4 is still out front, the 5 is inside the [..]

 

[macman2790]

?

Not sure where you are looking?

I split the 20 up into 4*5, the 4 is still out front, the 5 is inside the [..]

i just saw it right before you posted, thanks, like i said it's too late for math lol.

 

[swiftaw]

i just saw it right before you posted, thanks, like i said it's too late for math lol.

It's never too late for math 😀