Question

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

Answer 1

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

Explanation:

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))`