Here's the question you clicked on:
moongazer
find the derivative: Y(x) = 1/sqrt x please check my answer :)
|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|
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
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.
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 :)