anonymous
  • anonymous
Im trying to derive the following... ((4x+2)^2 - 4) / (x+1) And I use quotient rule to get...
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[\frac{ 8(4x+2)(x+1) - (4x+2)^2 -4 }{ (x+1)^2 }\]
anonymous
  • anonymous
But now I need help with simplification
welshfella
  • welshfella
you are correct so far

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welshfella
  • welshfella
well first expand those expressions in parentheses
ybarrap
  • ybarrap
Be sure you multiply out the numerator first and then simplify that. You will it cancel x+1 in the denominator and left with something simple.
campbell_st
  • campbell_st
well then factor the numerator (4x + 2){8(x + 1) -(4x +2)+4)} simplify the part inside { }
anonymous
  • anonymous
Oh alright
anonymous
  • anonymous
the inside would be 4x+10 right?
campbell_st
  • campbell_st
that's what I got
anonymous
  • anonymous
then do i expand those 2 brackets?
campbell_st
  • campbell_st
well it really depends... as the factored numerator is a correct solution... I'd leave it that way to avoid errors... but it really depends on what the question as for
anonymous
  • anonymous
it just asks for the derivative and apparently the answer is 16 but i can't get that
welshfella
  • welshfella
16?
anonymous
  • anonymous
yes
campbell_st
  • campbell_st
well there must be a condition and you have been given a value of x to substitute the question may ask for the slope of the curve at x = -2 or something like that
welshfella
  • welshfella
yep
anonymous
  • anonymous
Nope none of that
anonymous
  • anonymous
welshfella
  • welshfella
i think its 16 if x = 1 - if my simplification is correct
campbell_st
  • campbell_st
are you asked to find f '(1) or anything like that
welshfella
  • welshfella
f'(x) is a function of x
anonymous
  • anonymous
No xD lol
anonymous
  • anonymous
do you think it may be wrong?
welshfella
  • welshfella
then the answer cant be 16
welshfella
  • welshfella
yes - something is wrong...
campbell_st
  • campbell_st
well if you are asked for the derivative you have it correct. if you are asked to find the slope at x = 1 or f'(1) then you would need a numeric answer
LynFran
  • LynFran
u forget to take the derivative of the denominator that the problem here
anonymous
  • anonymous
Ohh i get it! I have to simplify the numerator before even differentiating it! Cause that way I get f(x) = 16x and f'(x) = 16
campbell_st
  • campbell_st
the derivative of the denominator is 1
welshfella
  • welshfella
yes thats right
anonymous
  • anonymous
\[f(x) = \frac{ 16x^2+16x+4-4 }{ (x+1) } = \frac{ 16x(x+1) }{ (x+1) } = 16x\]
ybarrap
  • ybarrap
Perfect! $$ f(x)=\cfrac{(4x+2)^2 - 4}{x+1}=\cfrac{16x^2+16x+4-4}{x+1}=\cfrac{16x(x+1)}{x+1}\\ $$ Now you see it: \(f'(x)=16\)
anonymous
  • anonymous
Yeah exactly!! Thanks so much for the help! :D
welshfella
  • welshfella
oh yes!!!! i missed that
welshfella
  • welshfella
what a crafty question!
anonymous
  • anonymous
Lol i know right! XD
welshfella
  • welshfella
well spotted
welshfella
  • welshfella
that function is a 'disguised' straight line with a slope of 16
anonymous
  • anonymous
Ahahaha xD yep!
welshfella
  • welshfella
you should be able to get 16 using the quotient rule but i didn't . There must have been an error in my work.

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