## anonymous 5 years ago find the derivative of y = sqrt(3)+(x)^1/3 + 1/x???

1. anonymous

$\sqrt{x}+x^{\frac{1}{3}}+\frac{1}{x}$?

2. anonymous

so the problem is A) $y=\sqrt{3+x ^{1/3}+1/x}$ or B) $y=\sqrt{3}+x ^{1/3}+1/x$

3. anonymous

or is first term $\sqrt{3}$?

4. anonymous

the b) style

5. anonymous

then do not be hoodwinked. $\sqrt{3}$ is constant, its derivative is 0

6. anonymous

yeap derivative of a constant is zero

7. anonymous

satelllite ur dis ans is wrong it does not tally wid de book pls explain in detail

8. anonymous

oh i did not give a complete answer. sorry. i only said derivative of $\sqrt{3}$ is 0 the others need power rule.

9. anonymous

(1/3)x^-2/3-1x^-2

10. anonymous

however, $\frac{1}{x}$ os a very common function, so you should just remember its derivative without using power rule. the derivative of $\frac{1}{x}$ is $-\frac{1}{x^2}$

11. anonymous

pls don't be angry at me cause i am in 11th and just a learner!!!!!!

12. anonymous

Guys I don't know how to write the equation here coz I am bad at latex stuffs

13. anonymous

k i will telll wat ans de book has

14. anonymous

comes up so often you do not want to compute it afresh each time. for $x^{\frac{1}{3}}$ youi use the power rule to get $\frac{1}{3}x^{-\frac{2}{3}}$

15. anonymous

I hope tejeshwar95 got the answer

16. anonymous

it says - 1/2*sqrt(3/x)+1/3*1/x^(2/3) - 1/x^2

17. anonymous

which is the same as $\frac{1}{2 \sqrt [3]{x^2}}$

18. anonymous

can't understand a thing

19. anonymous

sorry lets go slow. is the first term just $\sqrt{3}$ or is it $\sqrt{3x}$

20. anonymous

sorry for such a rude reply but i really can't get a hang of it!!!!! its sqrt(3x)

21. anonymous

ooooh then i apologize. i thought it was just $\sqrt{3}$

22. anonymous

its ok!!!!!!!!!!

23. anonymous

lets do them one at a time. you want to use the power rule, which says that the derivative of $x^r$ is $r\times x^{r-1}$ ok so far?

24. anonymous

wat is de power rule??? haven't heard bout it

25. anonymous

it tells you how to find the derivative of something raised to a power. for example the derivative of $x^3$ is $3x^2$

26. anonymous

ok?

27. anonymous

ok the 1 which says if y = x^n then n(x)^n-1

28. anonymous

yups got it till here!!!!!!

29. anonymous

yes that is the power rule.

30. anonymous

so the trick is to write each of these terms in terms of exponents and then use the power rule.

31. anonymous

k let me try it on paper hang on for a minute!!!!!!

32. anonymous

now $x^{\frac{1}{3}}$ is already written that way so that one is easy.

33. anonymous

i will wait.

34. anonymous

as far as $\sqrt{3}$ isconcerned we remove the 3??? cause we can't differentiate it???

35. anonymous

this one is the confusing one, but don't be fooled. $\sqrt{3x}=\sqrt{3} \times \sqrt{x} = \sqrt{3}\times {x^{\frac{1}{2}}}$ and a constant just stays there.

36. anonymous

k got it till here

37. anonymous

for example, the derivative of $x^2$ is $2x$ and the derivative of $\sqrt{3}x^2$ is $2 \sqrt{3}x$ the constant just says as a multiplier, so ignore it.

38. anonymous

k so i ignore sqrt(3)

39. anonymous

so only use the power rule on the $x^\frac{1}{2}$ part. bring out the exponent as a multiplier, and then subtract 1 from the exponent. i wait while you try it.

40. anonymous

but now did u take $\sqrt{3}x ^{2}$ come into picture

41. anonymous

u took it as an eg???

42. anonymous

that was just an example to explain that the $\sqrt{3}$ is unimportant. just a side example. not part of this problem.

43. anonymous

yes just eg.

44. anonymous

k now after trying i got 1/2*x ^-1/2

45. anonymous

yes!

46. anonymous

now convert back to radical from from exponential form.

47. anonymous

k correct till here sorry for being so slow

48. anonymous

no problems. long as you understand.

49. anonymous

do the same again??????

50. anonymous

do you know what $x^{-\frac{1}{2}}$ is in radical form?

51. anonymous

if not i explain, if so just convert back.

52. anonymous

nope not exactly

53. anonymous

ok. i explain. the exponent has a minus sign, so that means take the reciprocal. for example, $x^{-5}=\frac{1}{x^5}$

54. anonymous

yups got it

55. anonymous

the exponent is a fraction. the denominator is 2, so that means take the square root. the numerator is 1, so raise it to the power of 1, which is like doing nothing. so $x^{-\frac{1}{2}}=\frac{1}{\sqrt{x}}$

56. anonymous

therefore $\frac{1}{2}x^{-\frac{1}{2}}=\frac{1}{2\sqrt{x}}$

57. anonymous

so far so good?

58. anonymous

so we put $\sqrt{x^3}$ or $\sqrt{x}$

59. anonymous

in the denominator!!!!!!

60. anonymous

just $\sqrt{x}$ in the denominator. but also a 2 in the denominator because you are multiplying by 1/2

61. anonymous

and the numerator is this case is $\sqrt{3}$ because that constant is still there.

62. anonymous

can we have a voice chat???? dis is becoming a pain!!!!!!

63. anonymous

final answer: $\frac{\sqrt{3}}{2\sqrt{x}}$

64. anonymous

don't know how to voice chat. do you?

65. anonymous

nope

66. anonymous

voltage drops are happening i might not reply in between

67. anonymous

ok. the reason this problem is a pain for you is that you have to do three things: 1)convert to exponential form 2) use the power rule 3) convert back to radical form

68. anonymous

if u can hang around then give me some time i will just go through dese rules!!!!!!!!

69. anonymous

but you probably know what $7\times 8$ is because you have it memorized. since you are taking calculus, and since $\sqrt{x}$ is such a common function, you should probably memorize its derivative, which is $\frac{1}{2\sqrt{x}}$ that way you never have to do this again!

70. anonymous

saves you the three steps of writing in exponential form, using the power rule, and converting back. if you remember it then for homework or on a test you just write it.

71. anonymous

k learnt

72. anonymous

and derived

73. anonymous

and another very common function is $f(x)=\frac{1}{x}$

74. anonymous

its derivative is $f'(x)=-\frac{1}{x^2}$

75. anonymous

k got it

76. anonymous

but could not derive it!!!!!!!!

77. anonymous

note the "-" sign. you can do this using the power rule as well, but it never changes. $\frac{1}{x}=x^{-1}$ power rule gives $-1\times x^{-2}=-\frac{1}{x^2}$

78. anonymous

when do u come online tomorrow i am tired i need to relax!!!!!!!!!!

79. anonymous

or give me ur no if u live in delhi den i can talk 2 u over de phone!!!!!!!

80. anonymous

probably in the morning if you are here then. review power rule and of course exponents (because that is what it uses) in the mean time. good luck!

81. anonymous

no i am in us.

82. anonymous

k so wat's de time dere now????????

83. anonymous

thanx for ur help and the pains u took but if u cud come online at the same time as u came 2day den it wud be gr8

84. anonymous

ok i will try. look for me around this time or a little earlier.

85. anonymous

like wat's de time in US?? then i can guess wen 2 come online!!!!!!

86. anonymous

or can u hang around for a while ny the time i play a bit of COD

87. anonymous

k luks like i got it!!!!!!!!!!!

88. anonymous

ok i will be here for a while. have some work to do.

89. anonymous

i got the simplified form but ain't getin de full ans!!!!!!!!!!!

90. anonymous

to part 1?

91. anonymous

I got till see attachment

92. anonymous

93. anonymous

avoid the torn part look at the 1 written below!!!!!!!

94. anonymous

looks good to me. of course you still have actually subtract the exponents and convert back to radical form.

95. anonymous

how do i do dat pls tell!!!!!!

96. anonymous

lets do the middle one. $\frac{1}{3}x^{\frac{1}{3}-1}=\frac{1}{3}x^{-\frac{2}{3}}$

97. anonymous

so far so good?

98. anonymous

$\frac{1}{3}x^{-\frac{2}{3}}=\frac{1}{3\sqrt[3]{x^2}}$

99. anonymous

yups

100. anonymous

last one: $-1x^{-1-1}=-1x^{-2}=\frac{-1}{x^2}$

101. anonymous

yups

102. anonymous

luks like i got the whole answer

103. anonymous

and first one: $\sqrt{3}\frac{1}{2}x^{\frac{1}{2}-1}=\sqrt{3}\frac{1}{2}x^{-\frac{1}{2}}=\frac{\sqrt{3}}{2\sqrt{x}}$

104. anonymous

ok?

105. anonymous

yups

106. anonymous

now try and easy one for yourself.

107. anonymous

dude can u pls give me ur email id so dat de next time i have a doubt i can send it across or even chat again DUDE U ROCK!!!!!!!!! THANX FOR DE PATIENCE, SUPPORT.

108. anonymous

no problem. you can email me here. best bet to catch me.

109. anonymous

hold on i send an email address.

110. anonymous

If u don't mind can u even give me ur landline or phone no my parents won't mind if i called some1 who can really help me through sticky situations!!!!!!!! and by the way a must watch!!!!! http://www.youtube.com/watch?v=kVFdAJRVm94

111. anonymous

and another vid which if u can understand the music's nice i couldn't understand!!!!!!! http://www.youtube.com/watch?v=7zp1TbLFPp8&feature=mfu_in_order&list=UL

112. anonymous

Dude u online???? i hope i didn't harm ur feelings!!!!!!!!

113. anonymous

no no i am still here. you can email at satellite73.openstudy@gmail.com