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

- anonymous

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

- Stacey Warren - Expert brainly.com

Hey! We 've verified this expert answer for you, click below to unlock the details :)

- katieb

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

- anonymous

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

- anonymous

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

- anonymous

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- anonymous

the b) style

- anonymous

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

- anonymous

yeap derivative of a constant is zero

- anonymous

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

- anonymous

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

- anonymous

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

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

- anonymous

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

- anonymous

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

- anonymous

k i will telll wat ans de book has

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

- anonymous

I hope tejeshwar95 got the answer

- anonymous

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

- anonymous

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

- anonymous

can't understand a thing

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- 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?

- anonymous

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

- anonymous

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

- anonymous

ok?

- anonymous

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

- anonymous

yups got it till here!!!!!!

- anonymous

yes that is the power rule.

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

i will wait.

- anonymous

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

- 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.

- anonymous

k got it till here

- 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.

- anonymous

k so i ignore sqrt(3)

- 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.

- anonymous

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

- anonymous

u took it as an eg???

- anonymous

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

- anonymous

yes just eg.

- anonymous

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

- anonymous

yes!

- anonymous

now convert back to radical from from exponential form.

- anonymous

k correct till here sorry for being so slow

- anonymous

no problems. long as you understand.

- anonymous

do the same again??????

- anonymous

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

- anonymous

if not i explain, if so just convert back.

- anonymous

nope not exactly

- anonymous

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

- anonymous

yups got it

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

- anonymous

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

- anonymous

so far so good?

- anonymous

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

- anonymous

in the denominator!!!!!!

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

nope

- anonymous

voltage drops are happening i might not reply in between

- 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

- anonymous

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

- 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!

- 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.

- anonymous

k learnt

- anonymous

and derived

- anonymous

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

- anonymous

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

- anonymous

k got it

- anonymous

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

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

- anonymous

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

- anonymous

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

- 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!

- anonymous

no i am in us.

- anonymous

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

- 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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

to part 1?

- anonymous

I got till see attachment

- anonymous

##### 1 Attachment

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

so far so good?

- anonymous

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

- anonymous

yups

- anonymous

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

- anonymous

yups

- anonymous

luks like i got the whole answer

- anonymous

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

- anonymous

ok?

- anonymous

yups

- anonymous

now try and easy one for yourself.

- 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.

- anonymous

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

- anonymous

hold on i send an email address.

- 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

- 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

- anonymous

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

- anonymous

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.