## anonymous 3 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.

1. anonymous

@satellite73 can u help?

2. anonymous

@onegirl hints has been given in the ques so what will u get after simplifying ?

3. anonymous

ok hold on

4. anonymous

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. anonymous

last step is wrong u forgot to write in denominator?

6. anonymous

what step?

7. anonymous

for f'(x) = 3x^2 - 1?

8. anonymous

yeah

9. anonymous

ohh

10. anonymous

so 3x^2 -1/2x?

11. Mertsj

$f(x)=\frac{3}{2}x-\frac{3}{2}+\frac{1}{2}x ^{-1}$

12. anonymous

it will be 3x^2-1/2x^2

13. anonymous

okay

14. anonymous

so what do i do after that?

15. anonymous

16. Mertsj

$f'(x)=\frac{3}{3}-\frac{1}{2}x ^{-2}$

17. anonymous

so thats my derivative?

18. Mertsj

Whoops. Typo. Should be 3/2 not 3/3

19. anonymous

20. anonymous

okay ii guess not putting 2x^2 is why i got it wrong

21. anonymous

yeah

22. anonymous

thx

23. Mertsj

You were supposed to put 2x UNDER each term

24. anonymous

yea i did

25. anonymous

@Mertsj so i did it wrong?

26. anonymous

@zepdrix can u help please? did i do it right or wrong?

27. zepdrix

|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. anonymous

ok

29. anonymous

i see now

30. anonymous

yea i understand that step

31. zepdrix

So the x's will divide in the middle term. Do you understand how to simplify the first term?

32. anonymous

let me try

33. anonymous

i got (3x^2 - 3x + 1)/(2x)

34. Mertsj

Yep. Now split it up into 3 fractions like your teacher said.

35. zepdrix

ya you took a step backwards.. that was strange :c

36. anonymous

okay so i put 2x under each of those 3 fractions?

37. anonymous

i did?

38. Mertsj

Put 2x UNDER each term. The first term is 3x^2

39. zepdrix

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

40. anonymous

ok so 3x^2/2x - 3x/2x + 1/2x

41. anonymous

Ohhh okay got u

42. Mertsj

There you go.

43. zepdrix

yes, now simplify each fraction c: Don't combine them back together though! heh

44. anonymous

ok

45. anonymous

hold on lol sorry

46. anonymous

ok so i got 3x/2 - 3/2 + 1/2x after simplifying

47. zepdrix

k looks good c: Let's rewrite it in a way that will be easier to take a derivative of.

48. anonymous

ok

49. zepdrix

$\large f(x)=\frac{3x}{2}-\frac{3}{2}+\color{orangered}{\frac{1}{2x}}$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

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. anonymous

okay

52. anonymous

so now i can just find the derivative of 3/2 x - 3/2 + 1/2 x ^-1

53. zepdrix

yah sounds good.

54. anonymous

okay i'll find the derivative thx!