Simplifying the Product Rule for Derivatives

  • #1
lastochka
29
0
Hello,

I have this exercise that I can't get the right answer. I have to find derivative of

g(x)= (4${x}^{2}$-2x+1)${e}^{x}$

So, what is did is

g$^{\prime}$=(8x-2)${e}^{x}$+(4${x}^{2}$-2x+1)${e}^{x}$

My Prof said it is wrong... I am not sure if I have to multiply the brackets or what I did is completely wrong.
Can someone, please, check it for me?
Thank you!
 
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  • #2
Technically, it is not wrong, however, it can be simplified by factoring...what do you get when you fully factor?
 
  • #3
Thank you for answering! I am not sure how to simplify it by factoring...
 
  • #4
lastochka said:
Thank you for answering! I am not sure how to simplify it by factoring...

There is a factor common to both terms in your result...can you spot it?
 
  • #5
Yes, I see that, but will it make it simplified...
Here is what I have
${e}^{x}$(4${x}^{2}$-6x-1)
Is that it?
Thank you for helping!
 
  • #6
You are close...here's what I get:

\(\displaystyle g'(x)=(8x-2)e^x+\left(4x^2-2x+1\right)e^x=e^x\left(8x-2+4x^2-2x+1\right)=e^x\left(4x^2+6x-1\right)\)
 
  • #7
Oh, sorry I mistype, it is plus 6x not minus...
Thank you so much for helping!
 
  • #8
Good deal! Wouldn't you say that is simpler than the unfactored version? :D
 

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