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onegirl

  • 2 years ago

find the derivative of f(x) = (3x^2 - 3x + 1)/(2x). Directions, put 2x under each term and simplify. Then take the derivative.

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  1. onegirl
    • 2 years ago
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    @satellite73 can u help?

  2. niksva
    • 2 years ago
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    @onegirl hints has been given in the ques so what will u get after simplifying ?

  3. onegirl
    • 2 years ago
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    ok hold on

  4. onegirl
    • 2 years ago
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    after i put 2x over each term f(x) = 3x^2/2x – 3x/2x + 1/2x f(x) 3/2 x + 3/2 + 1/2x f’(x) = 3/2 + 0 - 1/2x^2 f’(x) = 3x^2 – 1

  5. niksva
    • 2 years ago
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    last step is wrong u forgot to write in denominator?

  6. onegirl
    • 2 years ago
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    what step?

  7. onegirl
    • 2 years ago
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    for f'(x) = 3x^2 - 1?

  8. niksva
    • 2 years ago
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    yeah

  9. onegirl
    • 2 years ago
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    ohh

  10. onegirl
    • 2 years ago
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    so 3x^2 -1/2x?

  11. Mertsj
    • 2 years ago
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    \[f(x)=\frac{3}{2}x-\frac{3}{2}+\frac{1}{2}x ^{-1}\]

  12. niksva
    • 2 years ago
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    it will be 3x^2-1/2x^2

  13. onegirl
    • 2 years ago
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    okay

  14. onegirl
    • 2 years ago
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    so what do i do after that?

  15. niksva
    • 2 years ago
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    it is ur answer

  16. Mertsj
    • 2 years ago
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    \[f'(x)=\frac{3}{3}-\frac{1}{2}x ^{-2}\]

  17. onegirl
    • 2 years ago
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    so thats my derivative?

  18. Mertsj
    • 2 years ago
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    Whoops. Typo. Should be 3/2 not 3/3

  19. niksva
    • 2 years ago
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    yeah thats your derivative

  20. onegirl
    • 2 years ago
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    okay ii guess not putting 2x^2 is why i got it wrong

  21. niksva
    • 2 years ago
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    yeah

  22. onegirl
    • 2 years ago
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    thx

  23. Mertsj
    • 2 years ago
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    You were supposed to put 2x UNDER each term

  24. onegirl
    • 2 years ago
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    yea i did

  25. onegirl
    • 2 years ago
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    @Mertsj so i did it wrong?

  26. onegirl
    • 2 years ago
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    @zepdrix can u help please? did i do it right or wrong?

  27. zepdrix
    • 2 years ago
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    |dw:1362685192013:dw|Do you understand this step? ~Splitting up the fractions. I wrote those ugly blobs to help show how we'll split it up.

  28. onegirl
    • 2 years ago
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    ok

  29. onegirl
    • 2 years ago
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    i see now

  30. onegirl
    • 2 years ago
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    yea i understand that step

  31. zepdrix
    • 2 years ago
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    So the x's will divide in the middle term. Do you understand how to simplify the first term?

  32. onegirl
    • 2 years ago
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    let me try

  33. onegirl
    • 2 years ago
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    i got (3x^2 - 3x + 1)/(2x)

  34. Mertsj
    • 2 years ago
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    Yep. Now split it up into 3 fractions like your teacher said.

  35. zepdrix
    • 2 years ago
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    ya you took a step backwards.. that was strange :c

  36. onegirl
    • 2 years ago
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    okay so i put 2x under each of those 3 fractions?

  37. onegirl
    • 2 years ago
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    i did?

  38. Mertsj
    • 2 years ago
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    Put 2x UNDER each term. The first term is 3x^2

  39. zepdrix
    • 2 years ago
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    You didn't "get" (3x^2 - 3x + 1)/(2x). You STARTED with that :) The first step was to split it into 3 fractions.

  40. onegirl
    • 2 years ago
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    ok so 3x^2/2x - 3x/2x + 1/2x

  41. onegirl
    • 2 years ago
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    Ohhh okay got u

  42. Mertsj
    • 2 years ago
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    There you go.

  43. zepdrix
    • 2 years ago
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    yes, now simplify each fraction c: Don't combine them back together though! heh

  44. onegirl
    • 2 years ago
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    ok

  45. onegirl
    • 2 years ago
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    hold on lol sorry

  46. onegirl
    • 2 years ago
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    ok so i got 3x/2 - 3/2 + 1/2x after simplifying

  47. zepdrix
    • 2 years ago
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    k looks good c: Let's rewrite it in a way that will be easier to take a derivative of.

  48. onegirl
    • 2 years ago
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    ok

  49. zepdrix
    • 2 years ago
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    \[\large f(x)=\frac{3x}{2}-\frac{3}{2}+\color{orangered}{\frac{1}{2x}}\]In the last term, we can bring the x up to the numerator by applying a negative exponent to it.\[\large f(x)=\frac{3x}{2}-\frac{3}{2}+\color{orangered}{\frac{x^{-1}}{2}}\]

  50. zepdrix
    • 2 years ago
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    Let's pull those X's off of the fraction bar, it will be easier to read if we just have coefficients in front of our X's. \[\large f(x)=\frac{3x}{2}-\frac{3}{2}+\frac{1\cdot x^{-1}}{2} \qquad \rightarrow \qquad f(x)=\frac{3}{2}x-\frac{3}{2}+\frac{1}{2}x^{-1}\]

  51. onegirl
    • 2 years ago
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    okay

  52. onegirl
    • 2 years ago
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    so now i can just find the derivative of 3/2 x - 3/2 + 1/2 x ^-1

  53. zepdrix
    • 2 years ago
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    yah sounds good.

  54. onegirl
    • 2 years ago
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    okay i'll find the derivative thx!

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