## moongazer 4 years ago find the derivative: Y(x) = 1/sqrt x please check my answer :)

1. moongazer

|dw:1347972647599:dw|

2. moongazer

I used the definition

3. anonymous

Yes, that seems essentially correct. However, I've never seen it written this way. Usually, we group up the Xs, so you'd get this : |dw:1347971974141:dw|

4. anonymous

or this : |dw:1347971995093:dw|

5. moongazer

What is the correct (best) way to right the derivative of a function? isn't it that there should be no radical in the denominator ? that's why I made it that way :)

6. mathslover

$\large{\frac{d}{dx}\frac{1}{\sqrt{x}}}$ $\large{\frac{d}{dx}{\sqrt{x}^{-1}}}$ $\large{\frac{d}{dx}x^{-\frac{1}{2}}}$ $\large{\frac{-1}{2\sqrt{x^3}}}$

7. mathslover

this is what I did. .. well do you mean by rationalizing? @moongazer

8. moongazer

yes, do you still need to rationalize it ?

9. mathslover

If u will then it will look ugly.. let it be in this way

10. ParthKohli

Yeah, you may rationalize if you need.

11. ParthKohli

Rationalizing beautifies the fraction; it doesn't make it ugly. lol

12. mathslover

or u can right : $\large{\frac{-1}{2x^{\frac{3}{2}}}}$

13. mathslover

lol $\large{\frac{-1\times x^{\frac{3}{2}}}{2x^3}}$

14. mathslover

$\large{\frac{-\sqrt{x^3}}{2x^3}}$ @moongazer

15. mathslover

got it @moongazer ?

16. moongazer

yes, based on your answers, Does it mean that you can write the derivative of a function in anyway you like as long as it doesn't change the meaning of your derivative? it could be in exponential,rationalized, not rationalized or any other forms.

17. moongazer

@mathslover

18. mathslover

yes

19. moongazer

Thanks :)

20. anonymous

Also, if you choose to keep it simply as $\frac{ -1 }{ 2x^{3/2} }$ is that it makes it simpler if you need to find its derivative after that (because sometimes, they just love to have you chain-derive something)

21. moongazer

Thanks for the info :)