How do you find the derivative of $ArcSin[x^(1/2)]$ ?

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Answer 1 · 2018-03-23T02:47:30

$d/dxsin^-1(x^(1/2))=1/(2sqrt(x-x^2))$

In general,

$d/dxsin^-1x=1/sqrt(1-x^2)$

In our case, due to the argument of the arcsine function, we'll need to apply the Chain Rule as well:

$d/dxsin^-1(x^(1/2))=1/sqrt(1-(x^(1/2))^2)*d/dxx^(1/2)$
$=1/(2sqrt(x)sqrt(1-x))=1/(2sqrt(x(1-x)))=1/(2sqrt(x-x^2))$

How do you find the derivative of ArcSin[x^(1/2)]ArcSin[x^(1/2)]?