find the derivative: Y(x) = 1/sqrt x please check my answer :)

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find the derivative: Y(x) = 1/sqrt x please check my answer :)

Mathematics
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|dw:1347972647599:dw|
I used the definition
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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or this : |dw:1347971995093:dw|
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 :)
\[\large{\frac{d}{dx}\frac{1}{\sqrt{x}}}\] \[\large{\frac{d}{dx}{\sqrt{x}^{-1}}}\] \[\large{\frac{d}{dx}x^{-\frac{1}{2}}}\] \[\large{\frac{-1}{2\sqrt{x^3}}}\]
this is what I did. .. well do you mean by rationalizing? @moongazer
yes, do you still need to rationalize it ?
If u will then it will look ugly.. let it be in this way
Yeah, you may rationalize if you need.
Rationalizing beautifies the fraction; it doesn't make it ugly. lol
or u can right : \[\large{\frac{-1}{2x^{\frac{3}{2}}}}\]
lol \[\large{\frac{-1\times x^{\frac{3}{2}}}{2x^3}}\]
\[\large{\frac{-\sqrt{x^3}}{2x^3}}\] @moongazer
got it @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.
yes
Thanks :)
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)
Thanks for the info :)

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