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anonymous

  • one year ago

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

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  1. anonymous
    • one year ago
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    \[\frac{ 8(4x+2)(x+1) - (4x+2)^2 -4 }{ (x+1)^2 }\]

  2. anonymous
    • one year ago
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    But now I need help with simplification

  3. welshfella
    • one year ago
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    you are correct so far

  4. welshfella
    • one year ago
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    well first expand those expressions in parentheses

  5. ybarrap
    • one year ago
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    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.

  6. campbell_st
    • one year ago
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    well then factor the numerator (4x + 2){8(x + 1) -(4x +2)+4)} simplify the part inside { }

  7. anonymous
    • one year ago
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    Oh alright

  8. anonymous
    • one year ago
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    the inside would be 4x+10 right?

  9. campbell_st
    • one year ago
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    that's what I got

  10. anonymous
    • one year ago
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    then do i expand those 2 brackets?

  11. campbell_st
    • one year ago
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    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

  12. anonymous
    • one year ago
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    it just asks for the derivative and apparently the answer is 16 but i can't get that

  13. welshfella
    • one year ago
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    16?

  14. anonymous
    • one year ago
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    yes

  15. campbell_st
    • one year ago
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    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

  16. welshfella
    • one year ago
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    yep

  17. anonymous
    • one year ago
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    Nope none of that

  18. anonymous
    • one year ago
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  19. welshfella
    • one year ago
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    i think its 16 if x = 1 - if my simplification is correct

  20. campbell_st
    • one year ago
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    are you asked to find f '(1) or anything like that

  21. welshfella
    • one year ago
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    f'(x) is a function of x

  22. anonymous
    • one year ago
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    No xD lol

  23. anonymous
    • one year ago
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    do you think it may be wrong?

  24. welshfella
    • one year ago
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    then the answer cant be 16

  25. welshfella
    • one year ago
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    yes - something is wrong...

  26. campbell_st
    • one year ago
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    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

  27. LynFran
    • one year ago
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    u forget to take the derivative of the denominator that the problem here

  28. anonymous
    • one year ago
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    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

  29. campbell_st
    • one year ago
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    the derivative of the denominator is 1

  30. welshfella
    • one year ago
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    yes thats right

  31. anonymous
    • one year ago
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    \[f(x) = \frac{ 16x^2+16x+4-4 }{ (x+1) } = \frac{ 16x(x+1) }{ (x+1) } = 16x\]

  32. ybarrap
    • one year ago
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    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: \(f'(x)=16\)

  33. anonymous
    • one year ago
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    Yeah exactly!! Thanks so much for the help! :D

  34. welshfella
    • one year ago
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    oh yes!!!! i missed that

  35. welshfella
    • one year ago
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    what a crafty question!

  36. anonymous
    • one year ago
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    Lol i know right! XD

  37. welshfella
    • one year ago
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    well spotted

  38. welshfella
    • one year ago
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    that function is a 'disguised' straight line with a slope of 16

  39. anonymous
    • one year ago
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    Ahahaha xD yep!

  40. welshfella
    • one year ago
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    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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