anonymous
  • anonymous
find the derivative of y = sqrt(3)+(x)^1/3 + 1/x???
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
\[\sqrt{x}+x^{\frac{1}{3}}+\frac{1}{x}\]?
anonymous
  • 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
  • anonymous
or is first term \[\sqrt{3}\]?

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anonymous
  • anonymous
the b) style
anonymous
  • anonymous
then do not be hoodwinked. \[\sqrt{3}\] is constant, its derivative is 0
anonymous
  • anonymous
yeap derivative of a constant is zero
anonymous
  • anonymous
satelllite ur dis ans is wrong it does not tally wid de book pls explain in detail
anonymous
  • 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
  • anonymous
(1/3)x^-2/3-1x^-2
anonymous
  • 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
  • anonymous
pls don't be angry at me cause i am in 11th and just a learner!!!!!!
anonymous
  • anonymous
Guys I don't know how to write the equation here coz I am bad at latex stuffs
anonymous
  • anonymous
k i will telll wat ans de book has
anonymous
  • 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
  • anonymous
I hope tejeshwar95 got the answer
anonymous
  • anonymous
it says - 1/2*sqrt(3/x)+1/3*1/x^(2/3) - 1/x^2
anonymous
  • anonymous
which is the same as \[\frac{1}{2 \sqrt [3]{x^2}}\]
anonymous
  • anonymous
can't understand a thing
anonymous
  • anonymous
sorry lets go slow. is the first term just \[\sqrt{3}\] or is it \[\sqrt{3x}\]
anonymous
  • anonymous
sorry for such a rude reply but i really can't get a hang of it!!!!! its sqrt(3x)
anonymous
  • anonymous
ooooh then i apologize. i thought it was just \[\sqrt{3}\]
anonymous
  • anonymous
its ok!!!!!!!!!!
anonymous
  • 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
  • anonymous
wat is de power rule??? haven't heard bout it
anonymous
  • 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
  • anonymous
ok?
anonymous
  • anonymous
ok the 1 which says if y = x^n then n(x)^n-1
anonymous
  • anonymous
yups got it till here!!!!!!
anonymous
  • anonymous
yes that is the power rule.
anonymous
  • anonymous
so the trick is to write each of these terms in terms of exponents and then use the power rule.
anonymous
  • anonymous
k let me try it on paper hang on for a minute!!!!!!
anonymous
  • anonymous
now \[x^{\frac{1}{3}}\] is already written that way so that one is easy.
anonymous
  • anonymous
i will wait.
anonymous
  • anonymous
as far as \[\sqrt{3}\] isconcerned we remove the 3??? cause we can't differentiate it???
anonymous
  • 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
  • anonymous
k got it till here
anonymous
  • 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
  • anonymous
k so i ignore sqrt(3)
anonymous
  • 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
  • anonymous
but now did u take \[\sqrt{3}x ^{2}\] come into picture
anonymous
  • anonymous
u took it as an eg???
anonymous
  • anonymous
that was just an example to explain that the \[\sqrt{3}\] is unimportant. just a side example. not part of this problem.
anonymous
  • anonymous
yes just eg.
anonymous
  • anonymous
k now after trying i got 1/2*x ^-1/2
anonymous
  • anonymous
yes!
anonymous
  • anonymous
now convert back to radical from from exponential form.
anonymous
  • anonymous
k correct till here sorry for being so slow
anonymous
  • anonymous
no problems. long as you understand.
anonymous
  • anonymous
do the same again??????
anonymous
  • anonymous
do you know what \[x^{-\frac{1}{2}}\] is in radical form?
anonymous
  • anonymous
if not i explain, if so just convert back.
anonymous
  • anonymous
nope not exactly
anonymous
  • 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
  • anonymous
yups got it
anonymous
  • 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
  • anonymous
therefore \[\frac{1}{2}x^{-\frac{1}{2}}=\frac{1}{2\sqrt{x}}\]
anonymous
  • anonymous
so far so good?
anonymous
  • anonymous
so we put \[\sqrt{x^3}\] or \[\sqrt{x}\]
anonymous
  • anonymous
in the denominator!!!!!!
anonymous
  • anonymous
just \[\sqrt{x}\] in the denominator. but also a 2 in the denominator because you are multiplying by 1/2
anonymous
  • anonymous
and the numerator is this case is \[\sqrt{3}\] because that constant is still there.
anonymous
  • anonymous
can we have a voice chat???? dis is becoming a pain!!!!!!
anonymous
  • anonymous
final answer: \[\frac{\sqrt{3}}{2\sqrt{x}}\]
anonymous
  • anonymous
don't know how to voice chat. do you?
anonymous
  • anonymous
nope
anonymous
  • anonymous
voltage drops are happening i might not reply in between
anonymous
  • 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
  • anonymous
if u can hang around then give me some time i will just go through dese rules!!!!!!!!
anonymous
  • 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
  • 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
  • anonymous
k learnt
anonymous
  • anonymous
and derived
anonymous
  • anonymous
and another very common function is \[f(x)=\frac{1}{x}\]
anonymous
  • anonymous
its derivative is \[f'(x)=-\frac{1}{x^2}\]
anonymous
  • anonymous
k got it
anonymous
  • anonymous
but could not derive it!!!!!!!!
anonymous
  • 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
  • anonymous
when do u come online tomorrow i am tired i need to relax!!!!!!!!!!
anonymous
  • anonymous
or give me ur no if u live in delhi den i can talk 2 u over de phone!!!!!!!
anonymous
  • 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
  • anonymous
no i am in us.
anonymous
  • anonymous
k so wat's de time dere now????????
anonymous
  • 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
  • anonymous
ok i will try. look for me around this time or a little earlier.
anonymous
  • anonymous
like wat's de time in US?? then i can guess wen 2 come online!!!!!!
anonymous
  • anonymous
or can u hang around for a while ny the time i play a bit of COD
anonymous
  • anonymous
k luks like i got it!!!!!!!!!!!
anonymous
  • anonymous
ok i will be here for a while. have some work to do.
anonymous
  • anonymous
i got the simplified form but ain't getin de full ans!!!!!!!!!!!
anonymous
  • anonymous
to part 1?
anonymous
  • anonymous
I got till see attachment
anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
avoid the torn part look at the 1 written below!!!!!!!
anonymous
  • anonymous
looks good to me. of course you still have actually subtract the exponents and convert back to radical form.
anonymous
  • anonymous
how do i do dat pls tell!!!!!!
anonymous
  • anonymous
lets do the middle one. \[\frac{1}{3}x^{\frac{1}{3}-1}=\frac{1}{3}x^{-\frac{2}{3}}\]
anonymous
  • anonymous
so far so good?
anonymous
  • anonymous
\[\frac{1}{3}x^{-\frac{2}{3}}=\frac{1}{3\sqrt[3]{x^2}}\]
anonymous
  • anonymous
yups
anonymous
  • anonymous
last one: \[-1x^{-1-1}=-1x^{-2}=\frac{-1}{x^2}\]
anonymous
  • anonymous
yups
anonymous
  • anonymous
luks like i got the whole answer
anonymous
  • 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
  • anonymous
ok?
anonymous
  • anonymous
yups
anonymous
  • anonymous
now try and easy one for yourself.
anonymous
  • 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
  • anonymous
no problem. you can email me here. best bet to catch me.
anonymous
  • anonymous
hold on i send an email address.
anonymous
  • 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
  • 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
  • anonymous
Dude u online???? i hope i didn't harm ur feelings!!!!!!!!
anonymous
  • anonymous
no no i am still here. you can email at satellite73.openstudy@gmail.com

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