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#1 2014-04-15 03:16:07

Shelled
Guest

Derivatives.

Find the derivative of
d/dx [(sin x)^(1/x)]

I don't think this is right, but here's my answer. I used the quotient & chain rule to get

(x^2 sqrt(x^2+7))/((x^5-3x^3+1)*sqrt(1-2x^3)) + (x sqrt (x^5 +3x^3+1)/((3 sqrt (x^2+7))(x^5-3x^2+1))

#2 2014-04-15 03:56:59

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 103,693

Re: Derivatives.

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

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#3 2014-04-15 05:08:34

Shelled
Member
Registered: 2014-04-15
Posts: 43

Re: Derivatives.

Sorry, hopefully this is more clear (the question, with some of my working out)

i.imgur.com/VyT9EPC.jpg

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#4 2014-04-15 05:33:24

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,548

Re: Derivatives.

hi Shelled

Welcome to the forum.

Thanks for the image.  You seem to have three different problems muddled up there.  Let's try this one:

Treat this as:

So this needs the chain rule only.

Hope that helps.    If that wasn't the problem, or you want more help, please post again.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#5 2014-04-15 10:00:47

Shelled
Member
Registered: 2014-04-15
Posts: 43

Re: Derivatives.

Whoops, there's a typo in the question; it's supposed to be

Could I still use the chain rule?

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#6 2014-04-15 10:03:35

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 103,693

Re: Derivatives.

Hi;

That is what I asked you in post #2.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Online

#7 2014-04-15 10:09:11

Shelled
Member
Registered: 2014-04-15
Posts: 43

Re: Derivatives.

Okay, sorry it's been a long day. I just realized that the working out I put up was for a different question too

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#8 2014-04-15 10:16:01

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 103,693

Re: Derivatives.

If you want to use the chain rule what would you pick?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Online

#9 2014-04-15 10:27:39

Shelled
Member
Registered: 2014-04-15
Posts: 43

Re: Derivatives.

Actually, not the chain rule.
Would I use the quotient rule?

Edit: wait. I'll stick with the chain rule I think I might know how to solve this. I'll post the answer in a bit.

Last edited by Shelled (2014-04-15 10:32:27)

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#10 2014-04-15 10:38:47

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 103,693

Re: Derivatives.

Hi;

Okay, post when you have it.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Online

#11 2014-04-15 10:58:14

Shelled
Member
Registered: 2014-04-15
Posts: 43

Re: Derivatives.

Okay, so not the complete answer, but am I going in the right direction?

and then apply the chain rule?

where

<--- not sure how to get the derivative of this. I think it's the product rule where...

and

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#12 2014-04-15 11:13:49

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 103,693

Re: Derivatives.

So far you are correct so see if you can go a little farther.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Online

#13 2014-04-15 11:46:01

Shelled
Member
Registered: 2014-04-15
Posts: 43

Re: Derivatives.

So I used the product rule; then applied it all to the chain rule and got

i.imgur.com/McRIMWE.png

having trouble with simplifying it though

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#14 2014-04-15 12:13:15

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 103,693

Re: Derivatives.

Hi Shelled;

That is correct! You could do a little simplifying though.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Online

#15 2014-04-15 12:19:23

Shelled
Member
Registered: 2014-04-15
Posts: 43

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#16 2014-04-15 12:23:08

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 103,693

Re: Derivatives.

Is that the answer they wanted?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Online

#17 2014-04-15 12:34:28

Shelled
Member
Registered: 2014-04-15
Posts: 43

Re: Derivatives.

I managed to simplify it to get the answer

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#18 2014-04-15 12:39:44

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 103,693

Re: Derivatives.

Okay, very good.  Welcome to the forum.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Online

#19 2014-04-15 12:50:15

Shelled
Member
Registered: 2014-04-15
Posts: 43

Thanks

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