Does anyone know how to find the derivative of f(x)=(sqrt(1/x^7)) the square root over the whole thing is confusing me

Question

Does anyone know how to find the derivative of  f(x)=(sqrt(1/x^7)) the square root over the whole thing is confusing me

hartnn · Answer

do you know the derivative of x^n ?

anonymous · Answer

no I dont think so

hartnn · Answer

$\large \dfrac{d}{dx}x^n=n \times x^{n-1}$

anonymous · Answer

well I know that if the square root wasnt over the whole problem, then wouldn't the answer be -7/x^6? I just am confused on the square root being over the whole thing

hartnn · Answer

how did u get -7/x^6 ?

hartnn · Answer

$\huge \sqrt A = A^{\frac{1}{2}}$

anonymous · Answer

$$\sqrt{(1)/(x^7)}$$

anonymous · Answer

so if the square root wasnt there wouldnt the answer be -7x^-6?

hartnn · Answer

i mean you have used the formula that i gave you to find derivative of x^7 , right ? 
but since we have square root, 
it'll be 
$\large x^{7/2}$

hartnn · Answer

in the denominator

hartnn · Answer

so, basically you are differentiating, 1/x^(7/2)
or 
$\large x^{-7/2}$

anonymous · Answer

thats the answer? I'm sorry I'm just confused lol

hartnn · Answer

thats what you will be differentiating.
what will u take 'n' as ?

anonymous · Answer

so it'd be -7/2x^-4.5?

anonymous · Answer

$$-7/2x^9/2$$

hartnn · Answer

yes! 
but keep -9/2 as it is
not 4.5

anonymous · Answer

Thank you so much! :)

hartnn · Answer

welcome ^_^

hartnn · Answer

since you are new here,
$\Huge \mathcal{\text{Welcome To OpenStudy}\ddot\smile} $
 if you have any doubts browsing this site, you can ask me.
Have fun learning with Open Study! :)

anonymous · Answer

Okay thanks again! :)