## moongazer Group Title find the derivative: Y(x) = 1/sqrt x please check my answer :) one year ago one year ago

1. moongazer Group Title

|dw:1347972647599:dw|

2. moongazer Group Title

I used the definition

3. m_charron2 Group Title

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. m_charron2 Group Title

or this : |dw:1347971995093:dw|

5. moongazer Group Title

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 Group Title

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

7. mathslover Group Title

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

8. moongazer Group Title

yes, do you still need to rationalize it ?

9. mathslover Group Title

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

10. ParthKohli Group Title

Yeah, you may rationalize if you need.

11. ParthKohli Group Title

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

12. mathslover Group Title

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

13. mathslover Group Title

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

14. mathslover Group Title

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

15. mathslover Group Title

got it @moongazer ?

16. moongazer Group Title

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 Group Title

@mathslover

18. mathslover Group Title

yes

19. moongazer Group Title

Thanks :)

20. m_charron2 Group Title

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 Group Title

Thanks for the info :)