Question

find the derivative of y = sqrt(3)+(x)^1/3 + 1/x???

Answer 1

\[\sqrt{x}+x^{\frac{1}{3}}+\frac{1}{x}\]?

Answer 2

so the problem is

A) \[y=\sqrt{3+x ^{1/3}+1/x}\]
or

B)
\[y=\sqrt{3}+x ^{1/3}+1/x\]

Answer 3

or is first term \[\sqrt{3}\]?

Answer 4

the b) style

Answer 5

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

Answer 6

yeap derivative of a constant is zero

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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 \[-\frac{1}{x^2}\]

Answer 11

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

Answer 12

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

Answer 13

k i will telll wat ans de book has

Answer 14

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

Answer 15

I hope tejeshwar95 got the answer

Answer 16

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

Answer 17

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

Answer 18

can't understand a thing

Answer 19

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

Answer 20

sorry for such a rude reply but i really can't get a hang of it!!!!!

its sqrt(3x)

Answer 21

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

Answer 22

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

Answer 23

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?

Answer 24

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

Answer 25

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

Answer 26

ok?

Answer 27

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

Answer 28

yups got it till here!!!!!!

Answer 29

yes that is the power rule.

Answer 30

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

Answer 31

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

Answer 32

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

Answer 33

i will wait.

Answer 34

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

Answer 35

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.

Answer 36

k got it till here

Answer 37

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.

Answer 38

k so i ignore sqrt(3)

Answer 39

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.

Answer 40

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

Answer 41

u took it as an eg???

Answer 42

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

Answer 43

yes just eg.

Answer 44

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

Answer 45

yes!

Answer 46

now convert back to radical from from exponential form.

Answer 47

k correct till here sorry for being so slow

Answer 48

no problems. long as you understand.

Answer 49

do the same again??????

Answer 50

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

Answer 51

if not i explain, if so just convert back.

Answer 52

nope not exactly

Answer 53

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

Answer 54

yups got it

Answer 55

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

Answer 56

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

Answer 57

so far so good?

Answer 58

so we put \[\sqrt{x^3}\] or \[\sqrt{x}\]

Answer 59

in the denominator!!!!!!

Answer 60

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

Answer 61

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

Answer 62

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

Answer 63

final answer:
\[\frac{\sqrt{3}}{2\sqrt{x}}\]

Answer 64

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

Answer 65

nope

Answer 66

voltage drops are happening i might not reply in between

Answer 67

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

Answer 68

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

Answer 69

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!

Answer 70

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.

Answer 71

k learnt

Answer 72

and derived

Answer 73

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

Answer 74

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

Answer 75

k got it

Answer 76

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

Answer 77

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 \[-1\times x^{-2}=-\frac{1}{x^2}\]

Answer 78

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

Answer 79

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

Answer 80

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!

Answer 81

no i am in us.

Answer 82

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

Answer 83

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

Answer 84

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

Answer 85

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

Answer 86

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

Answer 87

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

Answer 88

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

Answer 89

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

Answer 90

to part 1?

Answer 91

I got till see attachment

Answer 92

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

Answer 93

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

Answer 94

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

Answer 95

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

Answer 96

so far so good?