# Thread: VERY EASY derivative question

1. ## VERY EASY derivative question

Hello,

I have a very easy question :

$\displaystyle (2+(1/x^2))^{1/2}$

My final answer is $\displaystyle -1/x^3(2+1/x^2)^{1/2}$

Am I right or wrong ??!

Thank you

2. Originally Posted by ZaZu
Hello,

I have a very easy question :

$\displaystyle (2+(1/x^2))^(1/2)$

My final answer is $\displaystyle -1/x^3(2+1/x^2)^(1/2)$

Am I right or wrong ??!

Thank you
$\displaystyle \sqrt{2+x^{-2}} = (2+x^{-2})^{\frac{1}{2}}$

$\displaystyle -2x^{-3} \times \frac{1}{2}(2+x^{-2})^{-\frac{1}{2}}$

$\displaystyle -\frac{1}{x^3\, \sqrt{2+\frac{1}{x^2}}}$

I got it exactly like yours except that I have a -1 instead of a -2 :S

There is a step where two 2's cancel, and I get a -1 !

I just found this out from a buddy through yahoo answers : http://www.wolframalpha.com/input/?i...1%2Fx^2)^1%2F2

4. Originally Posted by ZaZu

I got it exactly like yours except that I have a -1 instead of a -2 :S

There is a step where two 2's cancel, and I get a -1 !

I just found this out from a buddy through yahoo answers : http://www.wolframalpha.com/input/?i=derivative+(2%2B1%2Fx^2)^1%2F2
Yeah, you're right, I forgot to multiply by 0.5 when deriving the square root

5. Hehe thanks for the solving the problem though, you helped me prove that the answer sheet is wrong ^^

Thanks

6. Originally Posted by ZaZu
Hehe thanks for the solving the problem though, you helped me prove that the answer sheet is wrong ^^

Thanks
You did it not me