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<a https://www.thestudentroom.co.uk/showthread.php?t=7467335'> Year 12s: what will be the first way you research your future options? >>
<a https://www.thestudentroom.co.uk/showthread.php?t=7467335'> Year 12s: what will be the first way you research your future options? >>
<a https://www.thestudentroom.co.uk/showthread.php?t=7467335'> Year 12s: what will be the first way you research your future options? >>

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product rule

cant seem to get from here y=(x2+1)(x−1)2y=(x^2 +1)(x-1)^2
to
dy/dx=2(x−1)(2x2−x+1)dy/dx = 2(x-1)(2x^2 -x +1)

any help?
Reply 1
Avatar for toby_ling
toby_ling
Give me a sec.
toby_ling
Give me a sec.

thanks for your time
Reply 3
Avatar for around
around
13
toby_ling
Give me a sec.


I'd prefer a tan.
Reply 4
Avatar for qgujxj39
qgujxj39
17
What have you done so far? Let u=x2+1u = x^2 + 1, v=(x−1)2v = (x - 1)^2, apply the product rule and then post your working so we can see where you've gone wrong/got stuck.

around
I'd prefer a tan.


That's awful. +repped
tommm
What have you done so far? Let u=x2+1u = x^2 + 1, v=(x−1)2v = (x - 1)^2, apply the product rule and then post your working so we can see where you've gone wrong/got stuck.



That's awful. +repped

lolz thats kinda the first thing I did, but im going nowhere fast, im getting stuff to the power 6 which is not good
2(x−1)(x2+1)+2x(x−1)22(x-1)(x^2 +1) + 2x(x-1)^2
Reply 6
Avatar for toby_ling
toby_ling
(x-1)^2
d/dx = 2(x-1)

=>
dy/dx = 2(x-1)(x^2+1)+(x-1)^2(2x) (Product Rule)
(Factorise)
= 2(x-1)[(x^2+1)+(2x)(x-1)]
= 2(x-1)[(x^2+1)+(2x^2-2x)]
= 2(x-1)(3x^2-2x+1)
Reply 7
Avatar for toby_ling
toby_ling
Not sure why I don't get the answer you've stated. My answer is wrong, btw.
Reply 8
Avatar for Swayum
Swayum
18
toby_ling

dy/dx = 2(x-1)(x^2+1)+(x-1)^2(2x)
= 2(x-1)[(x^2+1)+(2x)(x-1)]


That 2x doesn't belong - should just be x.
Swayum
That 2x doesn't belong - should just be x.

why, its confusing without latex
Reply 10
Avatar for Swayum
Swayum
18
clad in armour
why, its confusing without latex


Because he already took out a factor of 2 outside the square brackets.
Reply 11
Avatar for toby_ling
toby_ling
clad in armour
why, its confusing without latex

The factorisation takes the 2 out of the brackets.

Cheers Swayam!
Pheylan
Got it

2x(x-1)^2 + 2(x-1)(x^2+1)

Take out 2(x-1) from both terms

2(x-1) (x(x-1) + (x^2+1))
2(x-1) (x^2-x + x^2+1)
2(x-1) (2x^2 - x +1)

thanks a lot, it was just down to a bit of factorising after all :smile:
Swayum
Because he already took out a factor of 2 outside the square brackets.

kewlness
thanks a lot swayum and toby

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