Question

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

Answer 1

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

Answer 2

But now I need help with simplification

Answer 3

you are correct so far

Answer 4

well first expand those expressions in parentheses

Answer 5

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.

Answer 6

well then factor the numerator

(4x + 2){8(x + 1) -(4x +2)+4)}

simplify the part inside { }

Answer 7

Oh alright

Answer 8

the inside would be 4x+10 right?

Answer 9

that's what I got

Answer 10

then do i expand those 2 brackets?

Answer 11

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

Answer 12

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

Answer 13

16?

Answer 14

yes

Answer 15

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

Answer 16

yep

Answer 17

Nope none of that

Answer 18

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

Answer 19

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

Answer 20

f'(x) is a function of x

Answer 21

No xD lol

Answer 22

do you think it may be wrong?

Answer 23

then the answer cant be 16

Answer 24

yes - something is wrong...

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

the derivative of the denominator is 1

Answer 29

yes thats right

Answer 30

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

Answer 31

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: \(f'(x)=16\)

Answer 32

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

Answer 33

oh yes!!!!
i missed that

Answer 34

what a crafty question!

Answer 35

Lol i know right! XD

Answer 36

well spotted

Answer 37

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

Answer 38

Ahahaha xD yep!

Answer 39

you should be able to get 16 using the quotient rule but i didn't . There must have been an error in my work.