moongazer
  • moongazer
find the derivative: Y(x) = 1/sqrt x please check my answer :)
Mathematics
schrodinger
  • schrodinger
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moongazer
  • moongazer
|dw:1347972647599:dw|
moongazer
  • moongazer
I used the definition
anonymous
  • 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|

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anonymous
  • anonymous
or this : |dw:1347971995093:dw|
moongazer
  • 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 :)
mathslover
  • mathslover
\[\large{\frac{d}{dx}\frac{1}{\sqrt{x}}}\] \[\large{\frac{d}{dx}{\sqrt{x}^{-1}}}\] \[\large{\frac{d}{dx}x^{-\frac{1}{2}}}\] \[\large{\frac{-1}{2\sqrt{x^3}}}\]
mathslover
  • mathslover
this is what I did. .. well do you mean by rationalizing? @moongazer
moongazer
  • moongazer
yes, do you still need to rationalize it ?
mathslover
  • mathslover
If u will then it will look ugly.. let it be in this way
ParthKohli
  • ParthKohli
Yeah, you may rationalize if you need.
ParthKohli
  • ParthKohli
Rationalizing beautifies the fraction; it doesn't make it ugly. lol
mathslover
  • mathslover
or u can right : \[\large{\frac{-1}{2x^{\frac{3}{2}}}}\]
mathslover
  • mathslover
lol \[\large{\frac{-1\times x^{\frac{3}{2}}}{2x^3}}\]
mathslover
  • mathslover
\[\large{\frac{-\sqrt{x^3}}{2x^3}}\] @moongazer
mathslover
  • mathslover
got it @moongazer ?
moongazer
  • 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.
moongazer
  • moongazer
@mathslover
mathslover
  • mathslover
yes
moongazer
  • moongazer
Thanks :)
anonymous
  • 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)
moongazer
  • moongazer
Thanks for the info :)

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