# Thread: Where does the sign go?

1. ## 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!

2. ## Re: Where does the sign go?

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

3. ## Re: Where does the sign go?

Originally Posted by szucslaszlo
I am having trouble calculating a very simple derivative, namely the derivative of cos(1/x).
$\displaystyle \frac{d}{{dx}}\left[ {\cos \left( {\frac{1}{x}} \right)} \right] = \frac{1}{{x^2 }}\sin \left( {\frac{1}{x}} \right)$

4. ## Re: Where does the sign go?

Originally Posted by Siron
$\displaystyle \frac{d}{dx}\left(\frac{1}{x}\right)=\frac{-1}{x^2}$
Oh, I am so embarrased. Thank you!

5. ## Re: Where does the sign go?

Thanks for both replies!