Im trying to derive the following...
((4x+2)^2 - 4) / (x+1)
And I use quotient rule to get...

- anonymous

Im trying to derive the following...
((4x+2)^2 - 4) / (x+1)
And I use quotient rule to get...

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- anonymous

\[\frac{ 8(4x+2)(x+1) - (4x+2)^2 -4 }{ (x+1)^2 }\]

- anonymous

But now I need help with simplification

- welshfella

you are correct so far

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## More answers

- welshfella

well first expand those expressions in parentheses

- 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

well then factor the numerator
(4x + 2){8(x + 1) -(4x +2)+4)}
simplify the part inside { }

- anonymous

Oh alright

- anonymous

the inside would be 4x+10 right?

- campbell_st

that's what I got

- anonymous

then do i expand those 2 brackets?

- 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

it just asks for the derivative and apparently the answer is 16 but i can't get that

- welshfella

16?

- anonymous

yes

- 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

yep

- anonymous

Nope none of that

- anonymous

##### 1 Attachment

- welshfella

i think its 16 if x = 1
- if my simplification is correct

- campbell_st

are you asked to find f '(1) or anything like that

- welshfella

f'(x) is a function of x

- anonymous

No xD lol

- anonymous

do you think it may be wrong?

- welshfella

then the answer cant be 16

- welshfella

yes - something is wrong...

- 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

u forget to take the derivative of the denominator that the problem here

- 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

the derivative of the denominator is 1

- welshfella

yes thats right

- anonymous

\[f(x) = \frac{ 16x^2+16x+4-4 }{ (x+1) } = \frac{ 16x(x+1) }{ (x+1) } = 16x\]

- 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

Yeah exactly!! Thanks so much for the help! :D

- welshfella

oh yes!!!!
i missed that

- welshfella

what a crafty question!

- anonymous

Lol i know right! XD

- welshfella

well spotted

- welshfella

that function is a 'disguised' straight line with a slope of 16

- anonymous

Ahahaha xD yep!

- 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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