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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: 98,981

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.** **Thinking is cheating.**

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**Shelled****Member**- Registered: 2014-04-15
- Posts: 40

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: 7,378

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: 40

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: 98,981

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.** **Thinking is cheating.**

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**Shelled****Member**- Registered: 2014-04-15
- Posts: 40

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: 98,981

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.** **Thinking is cheating.**

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**Shelled****Member**- Registered: 2014-04-15
- Posts: 40

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: 98,981

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.** **Thinking is cheating.**

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**Shelled****Member**- Registered: 2014-04-15
- Posts: 40

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: 98,981

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.** **Thinking is cheating.**

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**Shelled****Member**- Registered: 2014-04-15
- Posts: 40

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: 98,981

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.** **Thinking is cheating.**

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**Shelled****Member**- Registered: 2014-04-15
- Posts: 40

Thankyou Got the right answer

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,981

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.** **Thinking is cheating.**

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**Shelled****Member**- Registered: 2014-04-15
- Posts: 40

I managed to simplify it to get the answer

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,981

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.** **Thinking is cheating.**

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**Shelled****Member**- Registered: 2014-04-15
- Posts: 40

Thanks

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