I am deriving g(x) = (1+4x)^5(3+x-x^2)^8.  TOPIC_SOLVED

Limits, differentiation, related rates, integration, trig integrals, etc.

I am deriving g(x) = (1+4x)^5(3+x-x^2)^8.

Postby MathStudent2011 on Fri Jun 24, 2011 8:35 am

I am deriving g(x) = (1+4x)^5(3+x-x^2)^8.

I get it all correct until the simplification part.
((20)(4x+1)(-x^2+x+3)^8+(8)(1-2x)(4x+1)^5(-x^2+x+3)^7)

Which the answer states as 4(4x+1)^4(3+x-x^2)^7(17+9x-21x^2)

Can't I just divide the section where I get stuck by the LCD of 4(4x+1)^4(-x^2+x+3)^7 giving me 20x^2+8x+10 ?
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Re: I am deriving g(x) = (1+4x)^5(3+x-x^2)^8.  TOPIC_SOLVED

Postby reesesloverb on Fri Jul 01, 2011 6:33 pm

You can factor the 4(4x+1)^4(-x^2+x+3)^7 out, but you can not drop it all together. Then you are left with:

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

if you foil 2*(1+4x)*(1-2x) properly and the distribute and reduce, you should end up with 17+9x-21x^2 for that section and 4(4x+1)^4(3+x-x^2)^7(17+9x-21x^2) as your overall answer.
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