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**Shelled****Guest**

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))

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,355

Hi;

Is this your problem:

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

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

i.imgur.com/VyT9EPC.jpg

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,586

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

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

Could I still use the chain rule?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,355

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.**

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,355

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.**

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,355

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.**

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,355

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.**

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,355

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.**

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

Thankyou Got the right answer

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,355

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.**

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

I managed to simplify it to get the answer

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,355

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.**

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

Thanks

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