Differentiation Troubleshooting: Solving for y = x * (x-1)^1/2

[aek]

I'm having difficulties in differentiating this question y = x . (x-1)^1/2 , i keep on getting answers different to the back of the book. If someone can help, thnx

 

[dextercioby]

Si it's

$$y(x)=x\sqrt{x-1}$$

...?Okay.What do you know about Leibniz (product) rule and the derivative of $x^{n}$ ?


Daniel.

 

[Dr.Brain]

Just apply the chain rule.Any of the available books can explain it to you.Maybe you are not reading and practising much.

 

[aek]

yes I am applying the chain rule, I am getting an answer but the same as the real one

 

[Hurkyl]

If you show your work, we can better help you see what you did wrong.

 

[aek]

No the question is -
$$y(x)=x\sqrt{x+1}$$

The answer is x(x+1)^1/2 +2(x+1) ALL OVER 2(x+1)

i get an answer which is the same but with an extra x(x+1)^1/2 on the numerator. can someone help please, or does anyone get the same answer

 

[jtbell]

To echo Hurkyl, show us how you got your answer...

 

[leon1127]

the way that i do it... if you don't want to use product rule
multiply the x back into the argument of the square root
u get y = (x^3-x^2)^0.5
then y' = 0.5((x^3-x^2)^(-0.5))(3x^2-2x)

 

[whozum]

$$x\sqrt{x+1}' = \sqrt{x+1}+\frac{x}{2\sqrt{x+1}}$$

$$f(x)=x, g(x) = \sqrt{x+1}$$

$$[f(x)g(x)]' = f'(x)g(x) + f(x)g'(x)$$

 

[dextercioby]

$$x\sqrt{x+1}' = \sqrt{x+1}+\frac{x}{2\sqrt{x+1}}$$

$$f(x)=x, g(x) = \sqrt{x+1}$$

$$f(x)g(x) ' = f'(x)g(x) + f(x)g'(x)$$

U mean

$$\left[f(x)g(x)\right]'\equiv\frac{d}{dx}\left[f(x)g(x)\right]=f'(x)g(x)+f(x)g'(x)$$

,right?


Daniel.

 

[whozum]

I put the apostrophe on the outside meaning the derivative of both f(x)and g(x) but parantheses would be better I suppose.

 

[dextercioby]

Mathematics is no gound for sloppy notations.Neither is physics...


Daniel.

 

[aek]

can someone tell me if anyone got the same answer as the book. I DID USING THE PRODUCT RULE BUDDY.

 

[dextercioby]

Either u didn't write the book's answer correctly,or it is incorrect.

$$(x\sqrt{x+1})'=\frac{2(x+1)^{3/2}+x\sqrt{x+1}}{2(x+1)}$$


Daniel.

 

[aek]

your wrong buddy.

 

[Hurkyl]

Can the attitude.

And I notice you still haven't posted your work...

 

[aek]

Can the attitude?
Let me first explain this to you, I've posted this 3 days ago, and yet i haven't go a decent answer. All u've guys have done is go around circles without touching the question. I used the product rule to its perfection. THATS MY WORKING BUDDY. If you think your some FBI trying to find out if i want you to the my homework then YOUR wrong. If you don't want to help with my question THEN don't post and waste my time. WHEN i help someone on this forum, i give 100%. Now how about you CAN your apathy and actually try to be a mentor like your supposed to be. BYE

 

[Hurkyl]

Yes, can the attitude.

Let me explain this to you: first, I'm sure you've noticed we have https://www.physicsforums.com/showthread.php?t=28 for homework help. To quote a specific line from them:

"So, post away--and show your work!"

Saying "I used the product rule to its perfection" is not showing your work.


Furthermore, I don't understand how you can be so utterly confident you did the problem perfectly that you absolutely refuse to show what you've done (so that, you know, we could find your mistake), and at the same time be so insolent when someone suggests that the answer to which you are trying to compare is wrong.

Either you're wrong (in which case you need to show your work), or the book's wrong. Actually, both could be wrong... but you seem to accept neither possibility.

 

[aek]

Either you're wrong (in which case you need to show your work), or the book's wrong. Actually, both could be wrong... but you seem to accept neither possibility.

As far as I'm concerned I'm on the lines with the guidelines. Must i remind you Hurkyl, this question isn't based upon the power rule alone. I know for a fact that i did the power rule correct but simplifying and getting neat is where i find trouble. And i asked did anyone else get an answer similar to the book. Honestly, Hurkyl, did you even look at the question? Once again Hurkyl, don't waste my time because i know for a fact you have no intention of helping people at all and I am pretty sure your position would of been put under review if someone else can spare soo much time on this forum (that time is indeed a waste).

 

[dextercioby]

What does the problem ask?Does it ask to simply differentiate the function $x\sqrt{x-1}$,or it asks for something totally different.

Daniel.

 

[aek]

differentiate in its most simple form -- if i forgot to state that, i ask for your forgiveness.

 

[Hurkyl]

I know for a fact that i did the power rule correct but simplifying and getting neat is where i find trouble.

It was the product rule last time, then the chain rule the time before that. But ignoring that inconsistency, I posit that the rest of us have no reason to share your level of confidence... especially because your description of what you got sounds quite unusual.

And, y'know, it would be nice if you would actually write what you got, instead of trying to give a verbal description.

And i asked did anyone else get an answer similar to the book.

Three different people answered. You ignored the first two, and to the third, you responded with "your wrong buddy." That's what I call an attitude problem.

(Correction: Two responded -- the third one I mentioned a correction to the second response which solved the wrong problem... or may have just been giving you an example to emulate with your problem)

im pretty sure your position would of been put under review if someone else can spare soo much time on this forum

You're welcome to talk to the management. You could PM someone directly, or use the "report bad post" feature, if you prefer. (It's the red triangle icon on the left of my post)

 

[dextercioby]

Since the problem is entirely subjective,i'll let u choose from the possible equal answers

1.$$\sqrt{x-1}+\frac{x}{2\sqrt{x-1}}$$
2.$$\frac{3x-2}{2\sqrt{x-1}}$$
3.$$\frac{(3x-2)\sqrt{x-1}}{2(x-1)}$$

Daniel.

 

[aek]

You're welcome to talk to the management. You could PM someone directly, or use the "report bad post" feature, if you prefer. (It's the red triangle icon on the left of my post)

Yeah i'll make sure i press that red triangle, pity, what are you going to do the whole day without harassing people over the net. Actually i didn't ignore the FIRST two answers, they were correct, they just weren't simplified. Concidently, that's where my problem lies. Describe the question verbally, well I'm sorry but I'm yet to professionalize my self with the LATEX system, so till then, i beg your pardon.

On the other hand, Dextercioby, you were close to the answer with your 3rd answer. Its suppose to be 2(x+1)+(x+1)^1/2. Neways, thnx guys for your help, but this is become rather a fight then a help forum, so i quit investigating this question, thanks.

 

[dextercioby]

It was with a plus,you changed it,i looked only at the first post.

There's not too much change

1'.$$\sqrt{x+1}+\frac{x}{2\sqrt{x+1}}$$
2'.$$\frac{3x+2}{2\sqrt{x+1}}$$
3'.$$\frac{(3x+2)\sqrt{x+1}}{2(x+1)}$$

The sqrt cannot be added in the numerator...

Daniel.

 

[Hurkyl]

Whoops, you're right Dex. Silly me making a correction when I was right in the first place.

Don't forget that other form you wrote down too:

$$\frac{2(x+1)^{3/2}+x\sqrt{x+1}}{2(x+1)}$$

 

[whozum]

He gave us two different problems, I just demonstrated how the produt rule works. The differnetiation is correct, whether you want to put it into one fraction or six millino fractions is your choice, the answers are equal, and if you ask me, the solution I gave (dex listed as #1) is the simplest.

 

[aek]

$$\frac{(3x+2)+\xsqrt{x+1}}{2(x+1)}$$

sorry this was an accident, look below

 

[aek]

Correct Answer is here,

$$\frac{2(x+1)+x\sqrt{x+1}}{2(x+1)}$$

It took my 4 days without a proper answer on PhysicsForum.com, however, it took less than 12 hours on a different forum which i refuse you people to join. Your all geniuses, CLAP FOR THE HANDICAPS.

 

[quantumdude]

aek,

In addition to having a serious attitude problem, you also have a severe misconception of what Physics Forums is all about. We don't supply homework solutions! We supply homework help. That means we work with you, not instead of you. That means you have to show your work.

Your all geniuses, CLAP FOR THE HANDICAPS.

Kid, you shouldn't talk. You're the one who needed 4 days to do this rather trivial problem. :rofl:

Edit to add:

And it wasn't even you who got the answer in 4 days! You got the answer from a different Forum.

 

[quantumdude]

Good Lord. I had locked this thread, thinking that it had run its course and that any future posts would just be more bickering from aek. But I can see now that this thread is not over, because...

$$\frac{2(x+1)+x\sqrt{x+1}}{2(x+1)}$$

This answer is wrong.

It took my 4 days without a proper answer on PhysicsForum.com, however, it took less than 12 hours on a different forum which i refuse you people to join. Your all geniuses, CLAP FOR THE HANDICAPS.

No, the correct answer was supplied by Dexter and Hurkyl, in posts 25 and 26, respectively.

My suggestion:

1. Ditch that other forum immediately.
2. Show your work from now on.

and oh yes:

3. Can the attitude.