Where does the sign go?

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December 9th 2011, 06:18 AM
szucslaszlo

Where does the sign go?

Hello there!
I am having trouble calculating a very simple derivative, namely the derivative of cos(1/x). I have came to the conclusion, that the result should be -sin(1/x)*1/x^2 = -sin(1/x) / x^2, but the result should be simply sin(1/x)/x^2. I don't understand how of why do we get rid of the minus sign. Thanks in advance!
December 9th 2011, 06:24 AM
Siron

Re: Where does the sign go?

$\frac{d}{dx}\left(\frac{1}{x}\right)=\frac{-1}{x^2}$
December 9th 2011, 06:24 AM
Plato

Re: Where does the sign go?

Quote:

Originally Posted by szucslaszlo

I am having trouble calculating a very simple derivative, namely the derivative of cos(1/x).

$\frac{d}{{dx}}\left[ {\cos \left( {\frac{1}{x}} \right)} \right] = \frac{1}{{x^2 }}\sin \left( {\frac{1}{x}} \right)$
December 9th 2011, 06:27 AM
szucslaszlo

Re: Where does the sign go?

Quote:

Originally Posted by Siron

$\frac{d}{dx}\left(\frac{1}{x}\right)=\frac{-1}{x^2}$

Oh, I am so embarrased. Thank you!
December 9th 2011, 06:28 AM
szucslaszlo

Re: Where does the sign go?

Thanks for both replies!

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