## MTALHAHASSAN2 one year ago can how we find the derivative of the following function 3sqrt x -1+x/x^4

1. anonymous

ill help but you also have to try.

2. MTALHAHASSAN2

ok sure

3. anonymous

4. anonymous

Now I need a medal

5. MTALHAHASSAN2

@Redneckk__Lifee but how you get that

6. anonymous

online duhh. and why did you ask my name you already know it.

7. anonymous

I'm pretty sure I'm waiting for a medal!!!!!!

8. marigirl

Okay so we are differentiating $\sqrt[3]{(x-1)}+ \frac{ x }{ x^4 }$ Is that the equation? I want to make sure its correct before we begin

9. marigirl

@MTALHAHASSAN2

10. MTALHAHASSAN2

@marigirl nope its wrong

11. marigirl

I meant- did i type your QUESTION correctly

12. MTALHAHASSAN2

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13. FireKat97

so its $f(x) = 3\sqrt{x} - \frac{ 1 + x }{ x^4 }$ ???

14. MTALHAHASSAN2

nope

15. FireKat97

no, I mean is that the question?

16. FireKat97

@MTALHAHASSAN2

17. MTALHAHASSAN2

yes it is

18. MTALHAHASSAN2

ok wait a sec

19. FireKat97

okay, so what you want to start off doing, is bringing the $x^4$ to the top, can you show me how you may do this?

20. MTALHAHASSAN2

@FireKat97 wait a sec

21. FireKat97

okay just tag me back whenever you're ready :)

22. MTALHAHASSAN2

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23. MTALHAHASSAN2

here is the question

24. MTALHAHASSAN2

ok so we need to find the derivative of this

25. FireKat97

so its just like the one I'd typed up above?

26. MTALHAHASSAN2

oh yeah know i see

27. FireKat97

so firstly you want to start off by bringing the x^4 up to the top, can you do this and show me what you get?

28. MTALHAHASSAN2

29. FireKat97

nah, no problem :)

30. MTALHAHASSAN2

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31. anonymous

haha

32. MTALHAHASSAN2

wait but why do we move 4

33. FireKat97

close, so I see you have brought up and distributed the x^4 and differentiated the 3x^1/2 and - x^-4, but you forgot about the - x^-3, do you see what i mean by this?

34. FireKat97

I find it easier to move it to the top, distribute it and then differentiate each of the terms

35. FireKat97

I'll show you what I mean

36. MTALHAHASSAN2

yeah plz i am confuse

37. FireKat97

$f(x) = 3\sqrt{x} - \frac{ 1 + x }{ x^4 }$ = $3\sqrt{x} - x ^{-4} (1 + x)$ do you see what I did here?

38. MTALHAHASSAN2

yeah know that's make a lot of scence

39. FireKat97

I simply brought the x^-4 into the numerator position and am now going to distribute it

40. FireKat97

yup so now we can distribute it like so $3\sqrt{x} - x^{-4} - x^{-3}$ and now we can differentiate each of the terms, have a go

41. FireKat97

do you see how I got that?

42. MTALHAHASSAN2

wait how you get -x^3

43. MTALHAHASSAN2

oh i got u

44. FireKat97

okay so when we open up $-x^{-4} (1 + x)$ we do $-x^{-4} (1) -x^{-4} (x^1)$ and according to index laws, when we multiply something with the same base, we add th powers, so for e.g. $(a^2).(a^3) = a^5$ so in the same way, $(-x^{-4}).(x^1) = -x^{-4 + 1} = -x^{-3}$

45. FireKat97

and now we have three separate terms, which we can differentiate

46. FireKat97

@MTALHAHASSAN2 did you try differentiating?

47. MTALHAHASSAN2

oh yeah i am trying it

48. FireKat97

oh okay :)

49. MTALHAHASSAN2

so are we left up with 3sqrt -x^-4 -x^-3

50. FireKat97

yup

51. MTALHAHASSAN2

and know we have to differentiating?

52. MTALHAHASSAN2

right

53. FireKat97

yeah we differentiate each of the terms

54. MTALHAHASSAN2

so for the sqrt is it be 1/2sqrt x

55. FireKat97

close

56. MTALHAHASSAN2

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57. FireKat97

yup thats right!

58. MTALHAHASSAN2

59. FireKat97

the $-x^{-4} - x^{-3}$??

60. MTALHAHASSAN2

is it goona go in the denominater

61. FireKat97

we haven't differentiated those two terms yet..

62. FireKat97

not quite...

63. FireKat97

do you want me to show you?

64. MTALHAHASSAN2

yes plz

65. FireKat97

okay so you know how we have $f(x) = 3x^{1/2} -x^{-4} -x^{-3}$ you did well in correctly being able to differentiate the first term, but we still have two terms left to differentiate so we should get $f'(x) = \frac{ 3 }{ 2\sqrt{x} } -(-4)x^{-4-1} -(-3)x^{-3-1}$ which can further simplify down to $f'(x) = \frac{ 3 }{ 2\sqrt{x} } + 4x^{-5} + 3x^{-4}$ does that make sense?