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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: 91,501

Hi;

Is this your problem:

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**Shelled****Member**- Registered: 2014-04-15
- Posts: 31

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: 6,648

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

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: 31

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: 91,501

Hi;

That is what I asked you in post #2.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**Shelled****Member**- Registered: 2014-04-15
- Posts: 31

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: 91,501

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.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**Shelled****Member**- Registered: 2014-04-15
- Posts: 31

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: 91,501

Hi;

Okay, post when you have it.

**In mathematics, you don't understand things. You just get used to them.**

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**Shelled****Member**- Registered: 2014-04-15
- Posts: 31

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: 91,501

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.**

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**Shelled****Member**- Registered: 2014-04-15
- Posts: 31

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: 91,501

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.**

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**Shelled****Member**- Registered: 2014-04-15
- Posts: 31

Thankyou Got the right answer

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

Is that the answer they wanted?

**In mathematics, you don't understand things. You just get used to them.**

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**Shelled****Member**- Registered: 2014-04-15
- Posts: 31

I managed to simplify it to get the answer

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

Okay, very good. Welcome to the forum.

**In mathematics, you don't understand things. You just get used to them.**

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**Shelled****Member**- Registered: 2014-04-15
- Posts: 31

Thanks

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